Buy a Bell Cable set for $8.00 on line and change all the cables, one at a time so you don't lose track of where they all go. You'll need a good quality set of diagonal cutters to cut the wire cable.

Rusted chrome can be cleaned with WD40 and 000 steel wool.
Rusted paint can be cleaned with Barkeepers Friend on a wet sponge.

At some point, the wheel hubs will need to be regreased. Look up procedures on youtube or sheldonbrown.com.

Good luck with improving your fitness and bike!