Buying a cheaper used bike to see if you enjoy and stick with cycling? Good idea.

Upgrading the components later? Unless you're only replacing 1 or 2 parts, it's almost certainly less expensive to just buy a whole new bike with the new stuff particularly if you don't already have the tools and knowledge to do it yourself - paying someone else to do it is rather expensive. However, 1996 isn't *that* long ago, odds aren't bad that there just won't really be any reason to change components.

If you posted a picture of the bike and the exact model I might be able to offer more specific advice.

P.S. That is assuming the bike is in good shape to begin with.