Poor Nico!! I had a three-legged cat once, too. It's tough for them to play when they're missing a hind leg, because they can't sit up or pivot the way they like to. Nico will have to build up his confidence and develop strategies for his new situation. To help, make sure he always has good footing when you try to get him to run or play--no uncarpeted flooring! You can also be creative about finding ways for him to play that don't require him to run or balance on his hind legs. I'd use a stuffed animal or puppet to wrestle with him (never your bare hand, as you don't want to encourage him to bite people). You can use 'Cat Dancer'-type toys and keep them close to him. You can also use the toys that are made to be stuffed with food or treats, so he has to bat them around to get the treats to fall out. Try using cat nip to exercise him, as well--most cats will roll around and all sorts of silly things if you spread a little on the floor.
As for choosing a food, it's tough to say. Most veterinarians will recommend prescription weight loss diets, because we know what's in them, and the companies guarantee that the caloric content won't change significantly from batch-to-batch. If your veterinarian does not think Nico needs a prescription diet food, ask about over-the-counter foods. If he or she doesn't have any suggestions, you can send me a list of products that are in your price range, and I'll see if I can find information on calories, nutritional value, etc for you. That information often isn't readily available--sometimes I have to call the company to find out what I need to know.
Good luck to both you and Nico!