Welcome to RCTALK.COM!!!
What a spectacular r/c to revive!!!
I'm a vintage guy too.

If you're planning to race, I'd start this project with a trip to your local tracks.
See what classes are running and what those rules are.
A vintage class may even require vintage gear!
If not and brushless and lipo's are in order, 2s system. There are lots of brands to choose from so be smart and buy once!
Track rules might dictate a hard-case battery pack, 17.5 or.13.5 motor, blinky esc and more.
Upgrading the radio is easy. Somewhat based on budget. If you're looking at low cost solid unit, ppl like flysky.
They also offer a Noble 4+ that suits most racers needs here.
I am prob going to buy a RadioMaster MT12. Steep learning curve but AMAZING capability!
The BEST news about your Schumacher is that there are YEARS of successful racing. Set up sheets for almost any track type should be easy to find!
I haven't been back to a track in years. If I ever actually get to race again, I plan to start slow in Novice classes and re-learn racing.
No sense being the fastest and first to slam the wall and break!
I don't imagine Schumacher vintage parts are any cheaper or easier to find than most others... research this WELL before you decide how fast is fast enough!
I can't wait to see your build!!!