Are all non-boss monsters tameable

I can tell you now there isn't a clear-cut winner for each role. But there are definitely monsters that excel more than others in their roles. Here's a list with some great monsters and why (this is partially taken from the official guide and partially my own experience):

Commandos:

• Chichu: Has very high strength stats and the valuable armor breaker and various "feeder" abilities.

• Dragoon: According to the guide the most cost effective monster (easy to max out and has some great abilities like Feral Speed 2, ATB charge 2, and Armor Breaker).

• Red/Golden Chocobo: Both have excellent potential but it would be wise to infuse them with pack mentality.

• Tonberry / Don Tonberry: They are amazing all-around Commandos but Tonberry is probably a bit better seeing as Don Tonberry continually has poison on him.

• Twilight Odin: Probably the most lopsided in stat growth and incredibly expensive to max out. However, once you do max him out his stats are almost peerless and he is one of the few monsters capable of a full ATB gauge of six elements.

Ravagers:

• Buccaboo: Great early peaker that is recruitable early game and the cheapest source of Gilfinder 2.

• Apotamkin: It's an early peaker with fairly high stats and has access to all elemental spells of the first two tiers and all physical strikes as well. Although the monster only has a 2% chance of being recruited.

• Blue Chocobo: Is the best choice for an ultimate all-around Ravager. Although you should try to infuse elemental spells that it does not learn naturally and infuse it with useful passives.

Sentinels:

• Pulse Knight: As an early game Sentinel it's the best and easy to max out. It also boasts the +25% HP passive which you can later infuse into another Sentinel.

• Bunkerbeast: Is a good choice for a long-term investment. It learns Challenge early on and boasts a massive HP pool (8000-ish). The only downside is that he doesn't learn Mediguard but you can infuse that ability.

• Silver Chocobo: Offers final stats similar to Bunkerbeast but at a lower cost. It's also the best chocobo to race with in Serendipity.

Saboteurs:

• Black Chocobo, Chelicerata, Necrosis, or Dendrobium. The first three have the improved debuffing passive. Dendrobium is a cheaper alternative and in all other ways just as viable.

Synergists:

• Amanojake: Notable only for infusion fodder learning all three of the en- spells which have high damage boosting potential.

• Gahongas: Earliest monster you will encounter that has both Bravery and Faith although you might be struggling to maintain its development.

• Yakshini: One of the better choices as your main offensive Synergist for a large portion of the game. It's fairly cheap to develop, relatively durable, and built for offense.

• Purple Chocobo: Best choice for a level 99 Synergist but given the advantages of narrow specialization you may wish to keep other Synergists as well.

Medics:

• Caterchipillar: Only natural bearer of the passive skill Resist Elements +30% and therefore makes for good infusion fodder.

• Flanitor: Probably the most accessible source of both Cura and Esunada and learns Improved Cure 2.

• Green Chocobo: Best candidate for a level 99 Medic: just be sure you infuse Esuna and Esunada from a Flanitor.

Omega is a COM with Late Bloomed (i.e. max level 99), Sparkprone, and Heartless.

Passives Abilities: Feral Surge, Feral Fatigue and Leadenstrike.

Starting Attributes:

Attack 595
Magic  479
ATB    Level 3
HP     3241