As long as the existing wiring is in good condition there I'm aware of no code requiring you to bring it to current standards when replacing devices. The undersized ground, if in good condition, should be OK. Check the continuity ground to neutral to see if it's good. You mentioned the grounds where twisted, you should crimp these. You are allowed to put 3 prong receptacles on an ungrounded system if you put the circuit on a GFCI, so if you want to be safe, do this for extra protection.
When replacing the outlets in wet areas like kitchens and baths always replace with a GFCI.
