It comes down to what is your budget and what are your expectations of the bike?

If you just want something practical some basic maintenance could go a long way in fixing some of your complaints. Cables/housing should fix the shifter issue and are very cheap to replace, for the being slow, it could be something as simple as not enough air in your tires, brakes rubbing or even bearings needing serviced but you should be able to make a 20 year old bike still work really well.

If you simply want an excuse to upgrade, I say go for it if the budget allows. If we are more excited about our bikes we tend to ride them even more which is always a good investment.