So, Final Fantasy XIII isn't everyone's favourite game, or even liked by most FF fans. However, I'm here to help light the way to the game by explaining which paradigms are best for each character and hopefully making people feel more comfortable within the battle system.
Character strengths
Lightning
She is the most versatile character in all the game. Lightning tends to do well in most roles so you can assign her most digms. She does best as commando or ravager but isn't so good at the rest. Keep Lightning in your party for most battles, except special circumstances, fights/bosses.
Sazh
This guy does great as a Synergist but can be swapped for a ravager or perhaps a sentinel but don't assign him anything else. Sazh is useful in parties since he tends to stay out of range of most enemies or gets dealt little damage. Recommended to have in your party if you are up against particularly strong enemies.
Snow
He is by far the best sentinel in the game. If need be he can make a decent ravager or commando. He is a pretty poor medic but better than Lightning or Fang. Snow has high HP and defence so he can withstand strong hits. He's really ideal for boss fights, even if he is not used as a sentinel.
Hope
Hope is a great medic and is much better than any other character and equally as good as a ravager or saboteur. Don't bother setting him as commando, he won't get you very far. Even though he is the best medic, he has really low HP. Use Vanille if you're facing a boss or strong monsters rather than using Hope.
Vanille
As a medic role she is almost as good as Hope but the best Saboteur. She is a decent ravager or synergist but don't assign her anything else. Is you use her as a medic equip the healing staff for an extra boost. If using black magic use her Belladonna/Malboro wand.
Fang
She makes a great commando next to Lightning and the second best sentinel as well as ravager and saboteur. She is a pretty flexible character like Lightning, so you can keep her in your party for the most part.
Paradigm decks
You can make up to six paradigms at any one time, the collection is called a paradigm deck or para-deck. What you choose to include in your deck should reflect your own personal fighting style, rather than following a set one. My para-deck could be absolutely atrocious for you to work with, but obviously works well for me. Try not to get too caught up in what is the 'best' strategy, the best should come from how you fight.
When you create a new party you are given a set of paradigms. You can manipulate these to how you wish or you can leave them as they are.
I hope this helps you all understand, perhaps even like the game!