Depends on what jobs you're playing, but a minimalist setup would be to just make a single set for both TP and WS (using each piece when it's superior to whatever else you have). I personally would aim for all 5 pieces with Acc/Attack +20, TA+2, and all but feet with STR/DEX+7, feet having WSD+3. I really only play THF and RUN though.
Examining each purpose you mention, you get:
TP solo: Really just for the Dual Wield, which means you don't have Trusts, which means you're probably farming Dynamis or Salvage. Up to you if you intend to spend money/inventory on farming gear.
TP with Party, TP high acc: Fairly ideal unless some of the newer pieces replace it. Hard to beat +20 accuracy and attack before even adding other bonuses in from leaf and dusk.
MAB: For Taeon, you can get +20 as an augment, but some pieces can be replaced with things like Shneddick Pants +1 and Highwing Helm. The hands could be augmented and get a total of +27 MAB which is pretty massive though.
Snapshot: I've been out of the RNG game for a long time so I can't answer this one as well, but I recall Snapshot appearing on a lot of gear, including some new pieces.
WS, STR/DEX, WSD set: Basically the same thing, right? These sets have fairly low base stats, especially when compared to AF/relic/empyrean, so even a stat like WSD can be trumped by +STR or something. WSD only helps certain WSs where STR/DEX covers a very wide spread, and would keep the augment useful for meleeing in too. You'd have to check some spreadsheets and calculators to determine which is better by WS.