The bulk of the rust on the frame seems to me to be surface. If you really want to do a bang up job, then go for stripping the paint. It doesn't seem entirely necessary, though, as you can use a light de-ruster on a rag and it'll scrub off with a little work.

As for the components, the brakes need new cables (and probably casings as well), the chain needs oiling, and really - that seems about it to make it ridable.

Check the spokes on the rim to see if they're loose and adjust where necessary. You'll be good in no time