.44 magnum would work, but would be a poor choice for a non expert, especially if you're planning to use a revolver. Best a good quality bolt action rifle between .243 and .308. A good quality scope is recommended as well. Then practice with it.
22 for squirrels because if you shoot them in the head, it wont damage the meat. For deer a 222 or 30 06. 12 ga slug if you live in a stupid state like Illinois like me and rifles are illegal to shoot deer with.