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.
I'm a fan of using the strips, both because it's flush to the wall (unscrew other hardware if needed) and because if it's not perfectly level you can pull it off and reattach to the backing strip. Works best if you apply to the frame with an inch or two of space from the edges so they're not visible after adjustments.
If it's a heavy frame you'll have to resort to finding a stud to drive a nail in, so pay attention to the weight limits on adhesive strips.
Cheap is just fine. You could probably use a palm-sized rock in a pinch. Gentle taps to go through drywall, it doesn't take much. If you happen to hit a stud, you'll know. Tap a little harder. You don't want to drive the hook into the drywall, and the nail into only drywall will be able to slide in and out if you mess with it - but don't. That just makes the hole a little bigger, increasing the chances that the nail will tilt and damage the drywall further.
Those picture hook nails may have a couple of little barbs on them to keep the nail from moving around in the hole. Again, tap it in, hook against the drywall, hang your picture.
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.
A4 and A5 says Europe to me. Are your walls drywall/gypsum board or are they something like lathe and plaster? Nailing into plaster can be unpleasant. Adhesive hooks might be better there.
Don’t buy either, and ignore the string. For little things that are not too breakable and assuming at least two weeks since painting, 3M Command Strips are amazing.
I typically use 3 per picture, to keep sides and top against the wall. Just adhere them to the back of the frame and literally place the picture where ever you like. Done. If you ever need to take them down, it’s just Velcro, and the sticky tape is a command strip the cones cleanly off the wall
look for a 16oz hammer. it's big enough for the biggest job you'll take on but not so big that it's unwieldy for smaller jobs like this one. if you can, spend a couple bucks more for something high quality that will last you a lifetime. buy once, cry once. eastwig is a great brand but there are others. maybe some other dads have good hammer brand recommendations too.
If you live in America near a harbour freight they are a great place to start for basic tools that you might not need all the time. For hanging pictures I'd also recommend a 12-16' measuring tape, a 6" torpedo level, and a pencil for marking where to put holes.