New DIY project: restoring this bike from the bins. How can I service this back wheel?
As there are balls missing and bent components, you should completely refurbish the hub.
It looks like a freewheel type hub rather than a freehub/cassette type. First thing to do is get the freewheel off. Personally I’d replace the freewheel so I’d be starting with unworn sprockets and chain.
Disassemble the hub, completely degrease and clean and inspect the cups and cones. If the bearing surfaces of the cups are damaged then you’ll need to consider a new hub (or even wheel as the rim is out of true). Check the axle is straight. Check cups, balls etc for wear. Ball bearing come in a few different sizes but presumably there are balls in the drive side which you can use to find out what size they are. The axle, cups, balls etc are all easily replaceable.
There is lots of bike repair glance on the web. I’m a fan of Park Tool Repair Help in general.
For your immediate problem, RJ The Bike Guy YouTube channel has a comprehensive video on refurbishing a freewheel hub that should show you everything you need to know about dealing with your hub.
Good luck with this project, it’s good to hear of someone bringing a bike back to life. You’ll learn a lot going through the process and will get great satisfaction from it.