Magic Item Creation Guidelines: +4 bonus to Caster Level
The Orange Prism Ioun Stone provides a +1 bonus to Caster Level, and requires no slot. Now, note that this does not specify that it is the Caster Level of one class; if you were a multiclass spellcaster with more than one spellcasting class (a mystic theurge, perhaps), the bonus would apply to all of your classes.
Moreover, an item that provides a bonus to Caster Level can be used by a Psionic character to get a bonus to Manifester level, by the rules of Psionics-Magic Transparency.
So a cerebremancer could use an Orange Prism to get +1 to both Caster Level and Manifester Level. That’s convenient.
Therefore, we want a +4 (or +6) version of the Orange Prism, but we’ll allow it to take a slot instead of having no space limitation.
The basic Orange Prism costs 30,000 gp.
Since Ioun Stones have no space limitation, they cost double what an item that does take up a slot costs, based on the Table: Estimating Magic Item Gold Piece Values. Thus a +1 bonus to Caster Level that isn’t an Ioun Stone should cost 15,000 gp.
Costs for bonuses are generally based on the bonus’s value squared, times some number of gold pieces. Since the Orange Prism is a +1 bonus, 12 = 1, so that number is 15,000 gp. So a +4 bonus would be
42 × 15,000 gp = 240,000 gp.
And a +6 version would be
62 × 15,000 gp = 540,000 gp.
Those are both enormous amounts of money; the latter takes almost all of the wealth of an 18th-level character (and most DMs do not allow you to put all your wealth in one item, and for good reason). Even at 20th level, the +6 bonus is more than half your expected wealth.
They are just guidelines after all, right?
The guidelines do not always provide a perfect value for all items; there are numerous cases where the formulas produce items that are much, much too expensive or much, much too inexpensive.
Here, though, it’s hard to argue with the forumulas. Bonuses to Caster Level are extremely valuable, and a +4 bonus is huge. They allow you to cast spells better than someone of your level usually could, which is just about the biggest deal, short of simply casting higher-level spells anyway. And with psionic augmentation, you basically are manifesting higher-level powers.
But wait, I’m a cerebremancer: I’m already behind
This is the big thing: to become a cerebremancer, you need at least three levels in each of the base classes, before taking levels of cerebremancer that advance both. Therefore, your Caster Level and Manifester Level are already three behind what a single-classed spellcaster or manifester would have. You aren’t really getting a bonus so much as catching up.
Thus, consider the effects of the 3.5 feats Practiced Spellcaster or Practiced Manifester: you gain a bonus to Caster Level or Manifester Level that may not exceed your total level. In other words, they let you “make up” missed levels, but don’t let you go ahead of where you would have been otherwise. This is a far, far less powerful effect, and more accurately describes what this item would do for you.
So let’s impose that limitation on the item:
When you wear these bracers, you get a +4 bonus to your Caster Level and Manifester Level, but this bonus cannot allow your Caster Level or Manifester Level exceed your total Hit Dice. You may have different bonuses for different classes depending on how close each is to your total HD.
Thus, as a Wizard 3/Psion 3/Cerebremancer 5
11th level, in total
Caster Level 11
3 Wizard levels + 5 Cerebremancer levels + 3 from the item
If you got the full +4, you would go over your HD
Manifester Level 11 as well (same calculation but with Psion levels)
If you later level up several times so that you are a Wizard 3/Psion 3/Cerebremancer 10/Loremaster 4:
Now, what would this item be worth? Still quite a lot, but it’s drastically limited compared to the full +4 item. The bonus is akin to taking two quite-good feats, but it’s only really useful to a cerebremancer and for them it’s quite crucial, so I’d favor pretty lenient pricing. Personally, bonus squared times 3,000 gp would be sufficient, though that’s largely because I would want to make it relatively easy to catch up; depending on your campaign and DM, I could see that number go as high as 6,000 gp. Anyway, with my own number:
+4 bonus (capped at HD):
42 × ~3,000 gp = ~48,000 gp
+6 bonus (capped at HD):
62 × ~3,000 gp = ~108,000 gp
For the sake of completion, a +3 version is the highest you need until 17th level, so:
32 × ~3,000 gp = ~27,000 gp
Obviously, still extremely expensive items, but they are extremely valuable to you.
Make sure you remember exactly what this bonus does!
A bonus to Caster/Manifester Level improves the spells/powers you can already cast/manifest: greater range, larger area, longer duration, more damage, anything that references “level” in the spell or power’s description. For psionics only, an increase in Manifester Level also increases bonus Power Points for having a high ability score and increases the limit on how many power points may be spent when Augmenting a power.
The bonus does not, however, increase your general spellcasting/manifesting ability. It does not give you more base spells per day or base power points, it does not allow you to cast/manifest higher level spells/powers, and it does not let you gain additional spells/powers known. An item that did that, even for a single level, even limited by your total HD, would be worth more than even a 20th-level character could afford. An item that did that should never be allowed into the game.
There are two systems for items in 4e. The original system and the new system.
In the original system there were two ways to acquire magic items. You either found them while adventuring or you bought them from a shop. The rules on what was available from a shop were pretty thin and left completely up to the DM's discretion. The limiting factor here was that you could only use a Daily item power once per milestone (2 encounters) completed.
However, when Essentials came out, there was a change. They introduced item rarity and all magic items now have a rarity (common, uncommon and rare) and they removed the restrictions on daily item powers. You can get common items the following ways:
Find a shopkeeper who stocks the item (DM discretion here), and purchase it for the listed gold cost (this is the cost listed on the item, the mundane weapon components are factored in here).
Enchant the item yourself using the "Enchant Magic Items" ritual or similar. For this you need a caster able to cast the spell at the level you need for the item, the item you'd like to enchant, and enough gold to cover the full cost of the enchantment (the item's cost).
Find them while adventuring.
Rare and Uncommon items can only be found while adventuring (though some DMs will make an exception and allow you to purchase Uncommon items with strings attached. Our DM uses a waiting period for current or near current level uncommon items).
To answer your question explicitly, yes, the players just pay the amount listed on the item (for common items). However, this is an opportunity to bust out the roleplaying and have them find a shop, if you want they can haggle with the merchant (and maybe get a better deal! (just not too good)).
As far as the cost, this is dictated not by the enchantment level (the +1), but by the item's level, so all L1 items are 360 gold, all level 2 items are 520 gp.
Best Answer
Bonuses of the same type don't stack, so it won't do anything for your +3 battleaxe, since the +3 is an enhancement bonus.
(Bonuses that have no type at all - i.e. a +2 bonus - stack with everything.)
EDIT: Note that there is no difference between bonuses based on the source. If you are making a roll or calculating a value, bonuses of type X don't ever stack, no matter what they are attached to.