Why do you want to change the crankset?
Your 2-3 shifting issue sounds more like the shifter (assuming you mean what I think you mean when you say it doesn't catch). My FD shifter on my 1992 Stumpjumper does the same thing (it feels like the shift lever isn't pulling the cable until the second or third pull). I only use that bike for crappy weather commuting so I haven't bothered to pull the shifter apart and figure out what is wrong.
My philosophy on chain/cassette/ring replacement is different than some others so take this for what it is worth. I would suggest that you just replace the chain for now. If you have jumping/skipping issues with the new chain, then replace the cassette. Otherwise, just ride it with the existing cassette until you have issues.