Hey Lauren,
22 lbs is pretty light for a steel bike. Fuji, Bianchi and Jamis still make steel road and touring bikes and they weigh about the same now as they did 30 years ago. Of course the carbon and Alu frames and forks are lighter, and much more popular.
I wouldn't worry too much about finding parts for older bikes... they are around, both new and used. I also wouldn't waste any time or money *fixing* an old Shwinn. If you can't ride it *as is*, skip it. Beyond brake pads, cables, tubes and tires.... just find another bike. Lucky for you, the world is full of old bikes!