I would do some research on what kind/brand of compound to use. I think I've used Meguiar's Diamond Cut in the past with good result. There seem to be many options. I think the best route is to start out with the minimally invasive approach - using a light compound first and just rub it in by hand to see where you end up. If it's not doing the trick you can try a more aggressive compound like the diamond cut with a buffer/polisher. I bet you might be able reduce a lot of that spotting and bring back some of that finish. If it doesn't work out, then you can always fall back on the repaint approach.

If painting turns out to be required, for sanding it sounds like you'll be ok with your basic AutoZone 3M type supplies. I think wet/dry with varying grits and perhaps some sanding sponges will be more than enough for what you need. If you check out AutoBody Toolmart you'll be amazed at the variety of products and options.