I'm with George. If there's something wrong, fix it and get it working. But there's no point spending a fortune on top of the range components for an entry level frame.
Also, bear in mind that when you buy a whole bike, it's always cheaper than buying it separately as a frame and components because the bicycle manufacturers buy components at a much lower price than they are available retail.
Often manufacturers may have several models at different prices that use the same frame, but have different components. It's not particularly economical to buy a bike with a great frame but with low end components with a view to upgrading them later, it will almost allways work out cheaper, in the long run, to buy one of the dearer models with better components fitted at the outset.
If you're buying new, look out for big discounts on "last years models". Other than the paint job, there's often not a lot of difference between one years model and the next. I bought a brand new 2007 model bike in 2008, and got about a 40% discount. In fact, going back to my point about component costs, with a 40% discount, I paid just £80 more for the whole bike than the frame alone would have cost.
Also, if you get really into cycling, it's not unusual to have more than one bike. If you do splash out on something more expensive, you might want to keep your Schwinn as a backup. I don't know whether you use your bike for commuting, or going to the shops, but for that sort of thing, you might want to save wear and tear on your "good" bike. Also, if you have to leave your bike locked up unnattended on occassion, it's no bad thing to use a cheaper bike. Even the best bicycle locks aren't that secure, so it's best to have a cheaper, less desirable bike in that sort of situation and use a good lock with it, so that it's too much effort for most theives to bother with.
I have pretty cheap "shopping bike", which I keep in good working order, but deliberately leave dirty so that it doesn't attract too much attention and I still use a pretty good lock with it. In fact, if I have to leave it for more than a few minutes, I use two locks, one a massive motorcycle D lock that would actually cost more to replace than the bike.