You need a different Free Hub body to go to 8 or 9 speeds. The 7 speed body is too short.
8 speed, you can use the same chain. 9 speed requires a new chain.
IF you are going to go to more speeds, I'd go directly to 9. Your Ebay prices won't be that much higher vs 8, and I think you'll find a better selection of cassettes for your riding type. plus the additional gear.