Light, Snow, Vanille. The leader switches around, though the vast majority of the game I lead with Light.

Reason? They're all my favorite characters. I hate Hope (hate hate hate), not a fan of how Sazh looks, and Fang is okay. Light & Snow are simply awesome, Vanille is a bit above average (the genki girl is pretty much always in my party in JRPG's anyways).

My paradigm sets change too much, couldn't tell you exactly. The only ones that were always up, were

COM / COM / RAV (max deeps)
RAV / RAV / RAV (chain build-up)

Lightning (leader), Fang (leader sometimes if i want to control SAB) and Hope

Paradigms at the moment are:
Aggression - (COM/COM/RAV)
Rel. Ass. - (RAV/COM/RAV)
Combat Clinic - (MED/SEN/MED)
Tortoise - (SEN/SEN/SEN)
Superiority - (SYN/SAB/SYN)
Infiltration - (SAB/SAB/SAB)

Only use Tortoise for ShaoLong and Long Gui, occasionally use Superiority for Cactuar Prime and Infiltration on anything that is giving me trouble which is usually only Guis.

Good tip for defeating Long Gui really quickly, POISON!!!! when they fall down inflict poison as the first De-Buff take off 50% HP a stagger or more :)

Like many, Lightning/Fang/Hope.

I'm kind of sorry for Snow, I like him more than Fang but her strength is just too much to miss on... I actually find her to have too few weak roles compared to the others.

I usually use Lightning, Fang, and Vanille. I just started controlling Fang instead of Lightning because she has more health and dies less often.

I do substitute Snow in for either Lightning or Fang on really tough battles where the enemy(s) have a very powerful attack, then just control Snow as when he is in his Sentinel role its almost impossible for him to die. Usually results in no stars, though!

I would use Hope more, but his health is so low. If I'm trying to be very "offensive" I switch him out with Vanille, though I don't notice all that much difference.

The only great use for Sazh I've found is Synergist and mainly casting Haste, but his offensive stats are terrible.

Right now I'm just grinding Alpha Behemoths for points and I use Light/Hope/Vanille and usually start with Com/Syn/Sab and then switch to Com/Rav/Rav as soon as Deshell and Deprotect are in place. Works fine for its simple purpose and the points roll in slowly but certainly (it seems to be the fastest way of leveling the crystarium at this point anyway).

Fang is a terrible Medic but apart from that she is actually quite useful, she knows most of the 'ra spells for Synergist and Haste which is the one you want and the only downside to her Saboteur is the lack of Poison/ga everything else she is very good at, especially Commando due to strength and Highwind which is amazing.

I just got my plat yesterday, 93 hours in. I made a big mistake by wasting 2.4 million gils buying 3 dark matters. Turned out the shao long gui's rare drop isn't that rare...Most of the game I used Lightning/Fang/Hope. But post game, I switched to Fang/Lightning/Vanille.

Fang for highwind...very helpful for farming the turtles when you haven't maxed out yet. She has crazy strength and very decent magic. Just can't ignore her.
Lightning has decent magic and strength so good in both ravager and commando role (besides, she has enfire which is really helpful against the Long Guis)
Vanille because she has more hp than Hope.....But I guess Hope would do as well.

It all depends on the strategies though. Sazh's blitz is also pretty awesome. Snow, well he's probably the only guy I didn't find much use for. I think I only used him for 1 fight, mission 64.

So, do most people here pick based mainly on stats, rather than how much they like the characters?

I'm kind of annoyed at how OP Fang seems to be, her finisher is better than Snow's, she has the most strength, and she sports -ra buffs.

My party throughout Chapter 10 onwards has been Hope/Lightning/Fang, the only problem being Hope has terrible HP, but he's using Nue, his ultima weapon, and his MAG is around 2.5k or so, and I haven't finished the story yet, 68 hours in, on Chapter 13, I was grinding for quite a while in Chapter 11 on Gran Pulse, lol.

When I'm grinding on Gran Pulse, I use Sazh/Snow/Fang, now, the reason being is that I have an AMAZING strategy to killing Adamantoise in around 1:30ish, which requires Sazh to have the Hyades Magnums, which have 1040 STR, I'd upgrade them to ultima, but an extra 30 levels for 10 STR isn't worth it... he also has 3 max Power Gloves at 250 STR each, and his STR is now at 3071, which is ridiculous DPS when he's COM, lol, the only problem is the Silk Tiger effect on the weapons, which lowers his HP to less than 5k, but hey, it's cool, he never gets hit. He's also amazing when fighting multiple mobs, his Blitz is THE SHIT.

So yeah... Sazh is by far the best character of the story.

Yeah, she's too good :/ Which is bad for me since I don't like her all that much. Since I haven't mastered everyone's roles though, I do switch to Snow and Vanille for defensive battles (Hope's a good medic but his HP is sometimes too low to live through, and for the time being I've specialized Vanille to medic).

I'm not very fond of Sazh so far, but I haven't started upgrading his stuff (items-wise) yet. He still seemed weaker than the rest earlier though... apart from the buffs.

At chapter 9's boss I wanted to have him in for the buffs but in the end (for 5 stars) I just ended up using shrouds and going for the usual members (well, at the time it was more like the most recent members, but I kept the setup later as well).