Just about any rear derailleur will work. I prefer Suntour, but that is just a personal choice. I really can't tell much from your picture.

The time and expense of a repaint on a bike of this grade is not worth it financially. Do a search on clean up, there has been a lot of success with some basic cleanup, polishing, and touch up paint.

If you are going to ride this bike much, do yourself a favor and take some of the money you save by not painting the bike and buy yourself a set of wheels with aluminum rims. Night and day improvement in the bike, and if you ever upgrade, you can swap the old wheels back on if and when you sell the bike.

I routinely see used sets of wheels (but I look every day) in the $20 to $30 a set price range.

If the only thing broken is the claw that mounts under the axle bolt, you can find replacements of that. But your picture also shows a jockey wheel missing, and a derailleur taking a hit like yours is likely bent.

You can buy a brand new lower end Shimano derailleur on line for around $10. Check out Niagara Cycle and others.