Should I upgrade?

Hi all, I've been commuter cycling for a few months now with a Schwinn Wayfarer that I picked up from a yard sale. I know Schwinn's are not the best out there by far, but hey, it was a good price at a yard sale for a woman who has not ridden in over 15 years.

Overall, it's ok.... it was not well assembled so I have been having to figure out a few things as I go and some of the pieces seem to come loose easily and I have already had to replace a few parts. Fortunately, we have a great co-op where I can have someone teach me for cheap, but it's still annoying to be riding and suddenly realized a screw is loose somewhere yet again!

Anyway, my question is this: Should I keep putting time and money into this bike to get around town, or would I be better off in the long run keeping an eye on craigslist for something more reliable? I know Schwinns are not good quality anymore, but since I have never had anything nicer, I have nothing to compare it to riding wise.

If I upgrade, what qualities/brands should I be looking for? Anything I should avoid? I ride around town, usually not more than 3 miles or so. I'm mostly trying to lessen my car usage. If it matters I am in Lexington, KY. We have some hills but the roads are pretty decent.