We got our pullup bar at Toysrus. It is designed for kids 5 and up. Ours has grips. It does have mounting hardware and you do need to mount this one. We placed it just high enough that my daughter could grab on to it standing on her toes. But its also too high for her to fit under the doorway for a pullover. We didn't want her to be able to do actual pullovers (or try them at this stage) in the door frame. We had one from Walmart, Gold's Gym, but it had a paper warning notice about a chemical that supposedly is in the set - I'm not sure where but it had bars and some other pieces for work on the floor. My daughter loves the bar.
One thing about the bar, though, is because it screws in (twists in), I have to have her face a certain direction so she doesn't inadvertently unscrew it as she works.