Well, I would strongly suggest you first talk to your local game warden and sheriff's department...as well as your local city laws, AND then your neighborhood laws...you will be answering to ALL of them. If there is no problems there, then you need to decide what kind of big cat you want...as a general rule of thumb, I personally do not like to keep anything that could readily end my life or eat me.
The species you choose will heavily influence the kind of foods you will feed. Another thing to consider (and something we take into consideration when feeding our cats), is the issue of feeding live...it is an ethical issue for a lot of people...but beyond that, feeding live brings them closer to their wild instincts (which never go away), and therefore, can make them more dangerous and definately less predictable.
Basically, until you have a species in mind, and have done a LOT more research on housing, laws, confinement, personality, and wether you can provide a good quality of life for a big cat, I really cannot be much assistance to you in speaking on issues of diet. That is one of the lesser things to consider in this very big venture.
