Bicycle Tutor

I have a Violet '65 Schwinn Varsity. It is in bad shape. I cleaned off the frame and it is in very rough condition. The top tube feels as rough as sand paper. How do I strip the frame? sand paper, steel wool... Then where do I find the paint and decals?

   

It looks like there's a substantial amount of rust on that bike, which may have eaten into the metal quite a bit. The drivetrain (particularly the chain) will need replacing, as well as some other parts. Have you tried removing the seat tube or handlebar stem? If you can't get those free it might not be worth restoring...
That said, if you still want to give it a shot you could get some toxic paint stripper at the hardware store. Apply it with a brush, wait a little while, and then scrub it with a wire brush. You may have to repeat the process a few times. It's really goopy and stings if it contacts your skin so you'd have to be very careful. An easier way would be to remove all the parts and take it to your local autobody shop for a $20-50 sand-blasting job.

Maybe there is some hope. The seat tube and handlebar stem are removable. Everything I have taken off has come rather easily. The only thing I am not sure how to remove is the hand brake on the handlebars

If you compress the brake lever and look inside you should see the top of a bolt. You'll need to loosen that to free the lever's clamp.

I have a related question. On an old 80s Schwinn Traveler that I just got from a thrift store, there is some light surface rust on the frame. Is there an effective way to perhaps clean up some of the rust without having to repaint the entire bike? Is there anything I could use to maybe touch up the paint? I read in a forum that soaking rags in vinegar and placing them around the frame may help in removing some of this surface rust. Another forum said that you could use steel wool to simply buff the rust out. Thanks so much for your help!

Here's a video about removing surface rust on chrome (with steel wool). It may not work that well on painted surfaces. Maybe try using some light sandpaper to get ride of the rust, and then touch it up with a similar color paint. A hardware store should be able to mix up a pretty close match for you.
I haven't heard if the vinegar/rag method works...

Oh yes on the subject of removing rust, I am concerned about the rust patches on my bike's frame (it's steel, probably of a poor quality because it was a cheap bike). I want to remove the worst of the rust and patch up the paintwork (I am in Wales, and it rains very frequently so this is quite important), any suggestions?

Have you finished this project yet? Did you end up repainting the frame, I have a local guy sandblast frames for me and then I repaint them myself. That would be my advice. Please post a pic of the schwinn if you've finished it. I'd love to see it.