The cover plate is a tricky one to get off, you have to take out the whole bottle stack, then unbolt each of the 9 rods that go to the back support, followed by taking off the plate that holds on the bottle gates. It's not that bad once you get into it, but the reassembly is a lot more difficult, as you have to get everything to align all at the same time. Take a lot of photos before and during, they will help you immensely during the reassembly. I have a bunch if you find yourself in a bind.
Any standard white works fine, if you are going to be painting the outside of the machine, then use the same paint. If not, even the regular Rustoleum gloss white will be good.
Here's a link to the manual, the machine family is the 56, 63, 90, 126 and 154, just be aware that there's some variants being a Vendorlator machine, so some cosmetic parts may be different (like the coin entry bezel)
http://www.vendoco.com/Documents/Slant%20shelve.pdf