I don't want to rain on your parade, but wheels are about the costliest parts on a bike, and replacing them and maybe a fork too could easily involve spending more than the bike is worth.

So unless this bike has lots of sentimental value, I suggest riding it as is, spending only small dollars to keep it going. Bikes have gotten much better in the intervening years with probably the best value for the buck being about 3-5 years ago, before China prices started to offset some of the gains. For less than the cost of upgrading this Varsity, you could get a nicer, lighter, better spec.d more recent used bike, and for not an awful lot more than that a decent new bike.