The summoned creatures are always different specific creatures unless the DM is using a variant that alters the standard summon spells

The Dungeon Master's Guide on Variant: Summoning Individual Monsters says that

When a character casts a summon monster or summon nature’s ally spell, she gets a typical, random creature of the kind she chooses. As a variant in your campaign, you can rule that each spellcaster gets specific, individual creatures rather than just some random one. This variant lets players feel more ownership over the creatures that their characters summon, but it entails some special problems, so don’t allow it without considering it carefully. (37)

The text then devotes another 500 words to this variant, the reproduction of all of which probably breaks some laws. Suffice it to say, it's complicated, but it has the advantage of being officially optional if that's a meaningful bar for your group.

If unconcerned with enhancement bonuses and only needing the weapon special abilities, the 1st-level artificer infusions personal weapon augmentation [trans] (Eberron Campaign Setting 117) et al. and personal natural weapon augmentation [trans] (Races of Eberron 188) et al. grant weapon special abilities to one of the creature's weapons or natural weapons.¹ A wand of personal weapon augmentation (1st-level spell at caster level 1) (15 gp/charge) is inexpensive enough that even if adding the magic weapon special ability brash (MIC 30) to one's unarmed strike every encounter, that will still be cheaper than having such as permanent magic weapon special ability using the methods below. The magic weapon special ability furious (OA 125) is in a similar but worse position, as such an effect can only be granted by a wand of weapon augmentation [trans] (ECS 117) (4th-level spell at caster level 7) (420 gp/charge), likely making long-term use too expensive to use such an item to consistently have, for example, furious fists.

If the enhancement bonus is desired, an alternative is finding a way to cast the 4th-level Drd spell superior magic fang [trans] (SpC 136). This is a very expensive wand (a wand of a 4th-level spell at caster level 20 costs 1,200/charge), but that 60,000 gp item grants all of the creature's natural attacks a +5 enhancement bonus and, by the time such a wand can be afforded, the character probably won't be participating in 50 more fights during his career.² Note that this also assumes the spell superior magic fang can affect unarmed strikes. (While the spell magic fang implies that spell can, the spell superior magic fang lacks such language.)

However, all these all run afoul of the opportunity cost needed to activate them, so I understand why you'd avoid them. Attempting to generate such effects faster makes the price higher and makes the options below even more appealing.

Let's do some math!

Amulet of Mighty Fists (DMG 246)
The amulet of mighty fists specifically improves both the wearer's unarmed strikes and the wearer's natural attacks, but only grants both enhancement bonuses on attack rolls and damage rolls.

Amulet of Mighty Fists
   Enhancement Bonus         Cost
          +1             6,000 gp
          +2            24,000 gp
          +3            54,000 gp
          +4            96,000 gp
          +5           150,000 gp

Unfortunately, the amulet of mighty fists apparently can't grant the wearer's unarmed strikes and natural weapons magic weapon special abilities (that is, at least it can't without DM permission).

Bracers of Striking (Magic of Faerûn 155-6)
These cost 1,310 gp, weigh 1 lb., occupy the bracers slot, and grant the wearer the ability to make unarmed strikes as if the wearer possessed the feat Improved Unarmed Strike (very carefully not granting the actual feat). They can be made magical as if they were a blunt double weapon (hence any magical enhancement bonus or special ability costs double, the text implying that each "fist" (or head, I guess?) can't be magicked separately).

Bracers of Striking        Cost
 Enhancement Bonus    (1,310 gp)+
         +1            4,000 gp
         +2           16,000 gp
         +3           36,000 gp
         +4           64,000 gp
         +5          100,000 gp
         +6          144,000 gp
         +7          196,000 gp
         +8          256,000 gp
         +9          324,000 gp
        +10          400,000 gp

The item is not as explicit as it could be (the bracers can be modified with additional magic weapon special abilities but don't say those affect the wearer's unarmed strike, and I've read at least one argument wherein it was said seriously that the bracers' themselves must be used to beat a fool to employ their weapon special abilities), but if one assumes the enhancement bonuses apply to unarmed strikes and one's only making unarmed strikes, the bracers are a better deal than the amulet of mighty fists.

Necklace of Natural Weapons (Savage Species 58)
This item affects but a lone natural weapon unless more cash is paid. It's acknowledge that unarmed strikes are not natural weapons (but there's a counterargument couched in the fanged ring, below), so this probably doesn't do you any good, but it's included for completeness because you asked. The cost is multiplied by the number of natural weapons the amulet affects.

Necklace of Natural Weapons  Cost to affects natural weapons numbering...
      Enhancement Bonus        One    Two    Three    Four    Five
             +1                  2      4       6        8      10
             +2                  8     16      24       32      40
             +3                 18     36      54       72      90
             +4                 32     64      96      128     160
             +5                 50    100     150      200     250
             +6                 72    144     216      288     360
             +7                 98    196     294      392     490
             +8                128    256     384      512     640
             +9                162    324     486      648     810
            +10                200    400     600      800   1,000

Costs are in 1,000s of gp. Also add to the cost
+(600 gp × the number of natural weapon affected).

This makes the necklace of natural weapons a better deal than the amulet of mighty fists only if the wearer has but one or two natural weapons, except that the necklace explicitly can have magic weapon special abilities, and the DM must approve the idea that magic weapon special abilities can be added via the amulet.

Other Options
Below are a few options unmentioned by your question.

• The fanged ring (Dragon Magic 101) (10,000 gp; 0 lbs.) doesn't say it can be further magicked to grant unarmed strikes enhancement bonuses or weapon special abilities, but a generous DM may allow it. Further, the fanged ring implies that an unarmed strike is a natural attack, so it's useful for attempting to convince the DM that a necklace of natural weapons really can affect one's unarmed strike.
• The ward cestus (Arms and Equipment Guide 6, 10) (10 gp; 4 lbs), an exotic weapon, says that attacking with it "is considered an unarmed attack," and attacks with it deal the same damage as the wielder's unarmed strike. If the DM permits the alternative class feature city brawler to fight with a ward cestus yet still be considered unarmed, this is a viable alternative.
• Just in case you later become concerned with enhancement bonuses, a Drd20 charges 600 gp to cast the 3rd-level spell greater magic fang [trans] (PH 250) on an unarmed strike (possible according to the 1st-level Drd spell magic fang [trans] (PH 250)). A Sor20 charges 8,500 gp to cast the 5th-level Sor/Wiz spell permanency [univ] (PH 259-60) on that greater magic fang spell. Although vulnerable to dispel magic effects, this combination is inexpensive enough to get done several times over the course of an adventurer's career before acquiring +5 enhancement in some other fashion is more prudent. (Costs are according to Spellcasting and Services (PH 129), but actually locating such powerful casters is campaign-dependent.)

"So what do I buy?"

If you're using only unarmed strikes, you'll need the bracers. Fortunately, some of the weapon special abilities you want only require the weapon to be wielded, so, for example, you could get the following:

• brash (MIC 30) (+1 bonus; 0 lbs.) furious (OA 125) (+2 bonus; 0 lbs.) fury (HB 130) (+1 bonus; 0 lbs.) bracers of striking (Mag 155-6) (65,310 gp; 1 lbs.). Note: The bracers' description says that they "may be modified with special weapon abilities as if they were a blunt weapon." Ask the DM if that means the bracers need a +1 magical enhancement bonus before they can have further magic weapon special abilities.
• +1 brash (MIC 30) (+1 bonus; 0 lbs.) furious (OA 125) (+2 bonus; 0 lbs.) fury (HB 130) (+1 bonus; 0 lbs.) ward cestus (AE 6, 10) (50,310 gp; 4 lbs.). Note: As an exotic weapon, the cash saved from buying a ward cestus will probably spent overcoming the −4 penalty for nonproficiency.

And if, for example, you bind the soulmeld girallon arms (Magic of Incarnum 68) to your totem chakra and want magic weapon special abilities for that soulmeld's four claw attacks, you'll need the necklace.

• fury (HB 130) (+1 bonus; 0 lbs.) necklace of four natural weapons (SS 58) (10,400 gp; 0 lbs.). Note: See the bracers Note, above, the necklace description containing similar vague language.

Note: The magic weapon special ability fury (HB 130) (+1 bonus; 0 lbs.) needs to apply to every natural weapon and unarmed strike for it to be worthwhile, yet the special ability deals but an extra +1d6 points of damage (albeit untyped) each and only while raging, so, really, I suggest just skipping that magic weapon special ability. The same and more goes for the weapon special ability berserker (MIC 29) (+1 bonus), and more being that the weapon special ability is limited to two-handed weapons (which, with an inappropriately large magical ward cestus, is a possibility but a silly and impractical one).

Other Useful Items

• The beast claws (SS 49) (9,610 gp; 1 lbs.) are a pair of +1 spiked gauntlets (PH 117, 118) that grant the wearer 2 claw attacks with a +1 enhancement bonus and, if the wearer already has claws, the enhancement bonus increases to +2 and the wearer's claws deal an extra +1d6 points of damage. Note: Combined with the soulmeld girallon arms, these are pretty spiffy, but, given the item's age (and provenance!), the DM will likely update the description for a contemporary campaign. However, any DM that allows these into the campaign may also allow them to be further magicked.
• The collar of venom (BV 114) (50,000 gp; 3 lbs.) causes the wearer's natural attacks to become poisonous (Fort DC 14, primary damage 1d10 Con, secondary damage 1d10 Con).
• The demonhair shirt (Dragon #356 69) (26,000 gp; 3 lbs.) grants the wearer immunity to fear, and the wearer can spend 2 rages simultaneously to enter a demonic fury that, among other effects, grants the wearer impressive bonuses that explicitly stack with rage and frenzy (!) and makes all the wearer's weapons (including natural weapons) chaotic for overcoming aligned DR.
• The gauntlets of ghost fighting (MIC 216) (4,000 gp; 1 lbs.), among other effects, causes the wearer's melee attacks to affect incorporeal creatures normally.
• The ghoul gauntlets (MIC 104-5) (10,000 gp; 1 lbs.) grant the wearer, before making an attack, the ability, once per round, to declare one natural or unarmed attack as capable of paralyzing a hit foe (Fort DC 13 negates).
• The ring of adamantine touch (MIC 121) (6,000 gp; 0 lbs.) causes the wearers weapons (including natural weapons) to overcome DR X/adamantine as if they were adamantine. Given its rarity, this is likely a late-game purchase if at all.
• The tentacle extension (illithid) (Und 75) (32,000 gp; 2 lbs.) grant a lone tentacle a +2 enhancement bonus on attack and damage rolls, a 1-step size increase to damage, and an extra 5 ft. of reach. Note: The soulmeld displacer mantle (Magic of Incarnum 64) bound to your totem chakra grants 2 tentacle attacks. However, that doesn't make this a good deal.
• The wyrmfang amulet (MIC 148) (1,350 gp; 0 lbs.) causes the wearer's natural attacks and unarmed strikes to overcome DR X/magic as if they were magic weapons. Given how frequently this arises, this is likely an early-game purchase, later sold when better options become available.

¹ Fortunately, the infusion personal weapon augmentation targets but a weapon and its description only mandates it affect a weapon, saying nothing about the weapon being manufactured, so affecting an unarmed strike should be a thing even if not a monk.
² This overstates things a little. The character'll probably need to buy two or even three eventually. Each wand contains sufficient charges to use 1 charge per encounter for about 3 levels worth of encounters. A third wand tips things in favor of the amulet over the course of the character's career.