I'll add my two cents. I have experience doing a few wall board jobs, replacing missing or broken boards. They turned out well, and I just finished patching a wall a week ago.
Yes, as noted earlier, you need premixed joint compound (mud) and LOTS of it. Unless you are a pro, stay away from the stuff you must mix. Start with a gallon and see whether this is enough. Do not use spackle, which is for small holes and things like that.
You must sand down the high spots, and then fill in the low spots. Expect to do at least three coats of mud, or more. Allow each coat to dry completely and then use a sanding screen to take down any high spots. When working with mud, sandpaper clogs up too fast. You attach the screen to a flat board like you would sandpaper, but you can bang it on a hard surface to knock off the excess dried mud. I find that stapling it to the board works well. Bend the screen over the edge and staple on the back side, with a staple gun.
I have not had trouble with mud sticking to paint. I never sanded low spots down to the paper surface of the wallboard, ever. Spread on a thick coat with a 4 to 6 inch putty knife. Then use something like a 12 inch knife to smooth it out. The trick is to remove a lot of mud, which you can then spread on other low spots. The more you take off here, the less you need to sand off with the screen. If it isn't perfect, and still has some low spots, let it go, and get it on the next coat. Don't spend time trying to make the first coats perfect.
On areas where the low spot is deep, the mud will shrink and you will need more coats than on thinner low spots. When you finish, use a coat of primer on the patched part of the wall. I like Acrylic water base primer. Once it is primed you may notice a few more blemishes, which you can fix with a little more mud. Once all the mud has been primed, and you are satisfied, you can paint with a finish coat.
Have fun. :