That bike appears to be in very good condition.

Varsities draw a lot of emotional responses. Some people hate them. Some love them. I don't hate or love them, but I respect them. They were very, very well built, but they're built to last rather than built to be fast. I suspect they were designed for 13 year old bikes who were sure to abuse their bikes.

Don't change much at first. In time, you'll know what you need to change. Tires are the first thing. Then maybe get some toe clips.

Money is better spent on a new bike. So keep this as your beater. If you want a fast bike, wait until you can afford it. This one will serve you for a lifetime if you just care for it.