Keep the schwinn until you can put together about $350. Then get a good used bike on ebay or Craig's list. With some looking you should be able to get a very nice late 80's, early 90's bike, that if it's been properly maintained will be a very nice bike.

It won't have integrate shifting, but you can find a bike with 14-16 speeds, lugged, butted frame,and firt rate componets for that price. and it will only weigh 2-3 lbs more than a modern cf wonder.