Replacing rusty crankset
Assumptions: the bike is a geared bike with a rear shifting mechanism that works okay.  You're looking to replace the chainring(s) on the front because they're rusted.  

If you keep the same number of teeth, then everything else will continue.

However if the chainring is worn, there's a good chance you'll need a new chain and new rear cassette as well.   Old and new parts don't play nicely on bikes, because they bed-into each other.

Also, if the cranks have rusted you might find the bottom bracket is in similar condition.  If you want it going and don't care about originality, just replace the whole bottom bracket with a cartridge.  So much nicer and easier, and often more water-resistant too.

The thing that will decide whether you want the same or slightly different sized chain rings is the front derailleur mechanism, in how far it can move and what differences it can cope with.   If you intend riding the bike on hills, a smaller inner ring might be a good change. Likewise, if you top-out then a bigger big ring might help.

The rear mech doesn't care so much about the front, it only cares about chainline.