I was recently able to borrow a hand planer from a friend.  It made a huge reduction in the amount of work needed to redo an outdoor cedar table top.  I think they run about 50 USD, which would quickly pay for itself if you have a lot of flat surfaces to clean up.

I have often used 60 grit sandpaper to successfully remove old paint, stain, or chipping surfaces on wood projects.  It always "works", but can take a long time and lots of sandpaper.  I was really impressed with how easy it was to strip an old cedar table top and do it by small bits at a time to a good precision with a hand planer.  I think the hand planer was adjustable to 1/64 of an inch.

One thing I did with the hand planer that I couldn't have done with sand paper was go across the boards to level out warpage.  Going across the grain did make the surface rough, but when I was satisfied with the height I then reduced the depth and went along the grain again to smooth it out.  Very pleased with the results.