A Univega will last you years if you take care of it. Most decent (i.e. around $500 or more new) bikes will last forever if you keep them up, replace stuff when it's worn, etc.
I started with a $150 wal-mart bike, rode it until it broke, fixed it, rode it some more, fixed it again, rode, replaced the frame, rode it some more, etc.... eventually I took those parts and put them on a touring bike frame, I expect it will last me dozens of years.
You don't have to spring for a nice bike initially, but be prepared, they will need upgrading and maintenance eventually.