I take it that isn't the actual machine? You're pretty much stuck with using a chemical stripper on the paint. The original finish would be shellac. With luck it will be intact under the paint and would have kept the paint from soaking into the pores. After the paint is stripped off it becomes a matter of repairing any damaged veneer and re-applying the shellac.
It's all very doable, it just takes time.
Make sure you post some pics of it when you get it and keep us informed of your progress. Knowing others are watching will help keep you motivated to finish it and you'll be glad you did when it's done.
Rodney