Haven't had much of a chance so far to really get my head around favourites, but my most common teams are...

Lightning/Sahz/Vanille - for the Sahz/Vanille commentary and all-round goodness you get out of it.
Lightning/Snow/Vanille - for sentinel-required battles
Lightning/Hope/Vanille - mmm, magey goodness

So basically Lightning and Vanille are my favourites in the heat of the battle, mostly for Lightning's badass-ness and Vanille being nice to look at, although the (kind of odd sounding) Australian accent making her moans when she casts can get annoying. Sahz/Vanille are just great together, really. I love it when they fight together. As for my favourite Paradigms... well, I use a lot, here are the most common ones for three people, anyway!

Relentless Assault (COM/RAV/RAV) is easily the most commonly used one. Decimates most enemies just by the constant tapping of the X button.
Diversity (COM/RAV/MED) for when I need a quick heal.
Solidarity (COM/SEN/MED) and Combat Clinic (MED/SEN/MED) are the most common ones I use for emergency situations when facing enemies that require a Sentinel.
Tri-disastor (RAV/RAV/RAV) combined with Salvation (MED/MED/MED) provide awesome awesome quick destruction & quick healing.
Aggression (COM/COM/RAV) is something I'm using a little more often lately as it's great for keepin' big solo enemies up in the air.

Others tend to only really get used for boss battles, and that's when you have to get a little more tactical, so things such as All For One, Hero's Charge, Bully, Thaumaturgy and Dirty Fighting can come into play.