are you tryna get the side covers to paint too?
The reason I'd recommend doing it "piecemeal" is to identify other problems which need to be fixed before buying new stuff. But if you're going full rebuild all new parts and committed to that cost, then yeah - go for it. It just bums me out if I put 800 bucks into new ignition and crank and cylinder and pipe and carb and get it all together only to realize the clutches are fucked up.
Read this: https://www.mopedarmy.com/wiki/Rebuild_a_Puch_E50_Engine
it's a different engine but generally pretty similar. with sachs you cannot use a piston stop, so hold the crank from turning other ways - lowest risk is a flywheel holder but that's another tool to buy plus I expect you intend to replace the whole ignition? maybe HPI? and it won't work with the HPI. moderate risk is a rope or similar shoved in the plug hole, or using something like a screwdriver through the flywheel holes, can be tricky depending on ignition, be carefu what you brace against. or brace the crank against the case with the jug off as in the linked rebuild tutorial.
you def want a flywheel puller. but u can also just hammer it off (but first research proper hammering-off-flywheels technique
other things, you probably want to have a Dremel to make all the parts you buy that don't quite fit actually fit, and to match cases and porting on the new cylinder.
An impact driver (even just a hammer type one) cuz the case bolts are probably stuck
i'd recommend welding tabs to the exhaust header to spring mount it up to holes drilled in the bottom cylinder fins, this makes the unreliable sachs exhaust mounting essentially a nonissue. you'd need 1 welder and 1 drill and 2 extra springs.
you'll want GOOD tire levers if you're changing the tires yourself, which you 100% should be.
likewise good cable cutters are a very useful item.
blind bearing puller or alternately a ball joint fork is really helpful for removing bearings from the crank
everything else I can think of is parts, not specialty tools. I'd recommend again the plugging the decomp and double nutting the clutch nut