Beaters are great to learn with....some of those really crappy ones resist maintenance so badly, you'll hone your skills and
decent parts will seem easy to fix (I'm referring to those plastic shifter units mostly here).
If you have a crank puller (I assume the Schwinn has square taper cranks) and the right bottom bracket tools (you'll have to look - some take a "pin" tool, others a weird notched wrench tool, or both, etc.) you can repack the bottom bracket bearings and ajust that.
Your stem should be easy to remove (may need to tap it with a rubber mallet if it's seized) and grease, and the heaset can be cleaned with a rag and repacked with grease if you have a large adjustable wrench and some other wrenches.
Yeah, if you have some basic tools you can probably do a good job with the bike. I like Le Tours actually - I'd fix it up and ride it if I had it
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Oh! And if nothing else replace all the cables and housing -- your shifting will feel like new and braking will be good.