He does look young.
I'm going to have to say mud turtle, I've caught a lot of snappers and he looks nothing like one. They're total jerks and I'm sure you'd figure it out soon if he was a snapper. He doesn't have the beak. His tail is longer, but snappers don't have flat shells like that.
The good news is that mud turtles are on the smaller range and easier to care for. All turtles are a challenge, but he should be easier than a slider.
You're going to have to pick up a basking lamp, and a full spectrum UVA/UVB light. Some people say only UVB, but a full spectrum would be better for him, note that some bulbs say full spectrum but only provide one of the two, so look for one that says it has both UVA and UVB.
For starters, romaine lettuce and earthworms are a good feeding start. Different species have different plant or animal preferences so that's something to look into.
You're going to want to pick up a high calcium turtle vitamin supplement. The calcium and the full spectrum light are crucial to keeping his shell from becoming sick and deformed.
A good solution to the tank issue is one of those huge rubbermaids, they usually provide enough space.
Does he look and act healthy? If his shell is firm, with no visible injuries, then you should provide him with enough water to swim and a land source that he can get up easily.