I would never run UV unless I had some serious parasite going on. I believe in dealing with the cause of the problem, not the symptoms. If you get rid of the cause, the symptoms will go away too. Clear water doens't mean your problem is solved, though it does look pretty.
My advice would be to do a big water change and manually remove as much of the algae as you can. Reduce your lighting period - If the algae is bad I'd do a lights off for a few days. Explain to your gf what's causing the overfeeding, and make sure she understands not to feed the fish. Take the fish food to work if you have to. Once you've got everything under control, you can look into ferts and co2 like alan suggested, though if you're wanting a low maintance tank, I'd possibly not do co2. Ferts are pretty low maintenance though.
Algae needs light, nutrients and oxygen. If you take away one of those things, it will go away. If you take away or greatly reduce 2 (light and nutrients) it will stop growing very quickly, then you can build back up to a level that you tank can handle while keeping algae growth to a minimum.
Regarding your new tank, if you're after cheap, get a second hand one - there are some great quality tanks out there for next to nothing, and besides, it's just a box to store your water in, right?
Good luck!