My Aunt painted her dark wood cabinets and they look great. It would definately be easiest if you took the hinges and knobs all completely off before you painted... and if they are stained or veneered you may want to invest in a stripper... the veneer or stain can come through the paint, I have some interior doors that are a bit yellowy from that. Primer is always a good investment.
If you are looking for some pretty decent cheap countertops, home depot is the place. You can get a 10' section probably under $100...precut miters or straight, its what I got for my house. They also have shorter sections. They carry some of the name brand coutertops in a couple stock colors for much cheaper than you can order them, only "problem" is less selection (good for me! it made it less confusing!).
Good Luck!