After you have stripped the paint off chemically and then touched it up with the sander (as you indicated you were) in preparations to paint it try to get an area that has little to no wind. It will inevietably blow dust and particles onto your paint. You wouldn't want that pretty paint job to have things in there that everytime you see them you think about it...

To paint it you can go somewhere like harbor freight and pick up an inexpensive paint gun for under $20. These work pretty good for projects liek this. A small portable air compressor is all you need to get the job done. Don't own one? Then you can rent them for a day easy enough.

When you get ready to get your paint, go into the autobody paint store tell them what you are painting they can recommend the best type brand in your price range. Remember when painting more layers less thick are better than less layers sprayed thickly. Takes a little longer but you will have more control over the overall quality. When two toning, a final coat or three of clear will keep things all smooth and durable.

Don't forget it is MOST important to grease the wheels/axles. Especially if it has been sitting up any length of time. These can lock up and you will end up beside the road in always the most inopportune time. Check those tires for dry rot. If you look at the sides of a trailer and there are miniscule cracks on the side walls, you should replace the tires. There may be great tread, but that doesn't mean they will last any time at all.

HTH.