How does one upgrade a bicycle?
Cranks and chainrings are made of aluminium, which does not rust. You'll probably be fine with cleaning them and new cassette and chain. This isn't that expensive any more. From quick googling, your bike uses 7-speed cassette, which are still available.

Upgrading to modern parts would require replacing all transmission components, shifters, derailleurs and the rear wheel. This will be expensive and probably not worth the trouble.