Dads for a minute for children who need a dad figure
The rule for every tool: first time buy cheap, second time buy good.
What that means is, get a cheap hammer. Maybe you use it twice and don't care. But if you use it so much it breaks, then you clearly need to buy a good one.
Harbor Freight is a good place for cheap tools.
I've recently discovered hard wall picture hooks. They hammer into brick and stay put. I used to drill and put a screw in - these are so much easier!
For plasterboard walls the standard picture hooks which come with nails are fine.
If it's a particularly heavy or valuable picture I'd probably still recommend drilling and putting a screw in in either type of wall.
I would say get a small kit of picture hangers. These are flat pieces of metal bent into little hooks, with a hole through them at about a 45 degree angle, along with nails that fit through those holes. These allow you to hammer the nail into drywall at an angle, then hang your picture frame wire on the metal hook. The angle makes it so that the nail doesn't pull out of the wall or dig down through the drywall.
Any small claw hammer will do.
Alternatively, you can get those small hooks with adhesive backing. 3M makes their quick-release adhesive strips. These are great if you live in a dorm or a rental or for any reason you don't want to put holes in the wall. The adhesive strip will have a little loose tag end on it, that you pull straight down parallel to the surface it's stuck to to release it.