I'm not sure if there's a single "best place" for farming, but I definitely recommend completing sidequests if you want to power up. It's more interesting than grinding and you get bonuses along the way.
In terms of maximum impact for minimum fuss, I recommend Goblin Chieftain, Cloudburst, and Dragoon for the final boss sequence. That gives you a SEN and a RAV whose feral links cover your buffs, plus a powerful COM that is cheap to max out and good without infusion.
Yeah I mean use the crystarium when I say leveling. If you search around here you can find a guide for optimizing your crystarium. I didn't bother with that and was still able to beat everything in the game + DLC. it's kinda hard to mess up, but if you want the very strongest....
Here's the best place to look for monster infusions: http://www.gamefaqs.com/ps3/619315-final-fantasy-xiii-2/faqs/63731
This guide has been built and discussed by many of the boards most knowledgeable members (not me haha). It'll tell you everything you need to know about monsters and how to infuse them.
some pointers: 1. Learn what the yellow and red locks are on monster abilities and how to manipulate them (in the guide).
2. it doesn't mater what you feed your "feeder" monsters (monsters you raise only to feed to another monster for it's ability). ONLY abilities can be transferred, no stats.
3. if you don't have the snow DLC then DO NOT goof up your chichu. Feed him ONLY strength mats and follow the guide very closely when infusing him. He is a one time only monster unless you get the snow DLC.
Flanitor is a good Medic, but I don't recommend using a monster Medic for the final boss sequence. At lower development you want SEN/RAV/COM, and at higher development you want SYN/RAV/COM (best SYNs for this are Yakshini and Sahagin Prince). Noel and Serah are more than adequate as Medics, or you can use Potions + Grimoire Hat quite effectively.