Millsi, this comes across as a really strange project. First, I do not think your mower would bring $20 on ebay, it is in worse condition than most of the ones abandoned by the roadside. Second, if it were miraculously repaired to good condition for a Rover of that model, it would probably only bring a bit over $100. Now, I've had a Rover like yours, in good condition, and I rather liked it, but I would never have spent more than say $100 to repair it - if it fell in a heap I'd have replaced it. In fact, I walked past a good one like yours, thrown out on a nature strip, a few weeks ago. (I've moved on from Briggs engines, I only like OHV Hondas now.)
The point I'm trying to make here, is that the practical, cost effective way to fix your Rover is to replace it with a much less knackered Rover, for $100 or so. If you see one on a nature strip of course, it will cost nothing.