I agree with Kimberly. WD40 is good for friction points, but not as a cleaning agent.
I have restored several presses. Taking it apart is not a bad thing at all. You can clean the pieces with a good degreaser like simple green or greased lightning. Use a fine steel wool with some of that 30 weight oil to buff off any rusted spots. If you need new paint, degrease again and paint with a Rustoleum, like matte black.
When you clean really well, it is very important to re-oil the various joints before putting it back into use. For most spots the 30 weight oil will work great. Look for the lubrication holes, sometimes painted red, above a joint, and squirt the oil in. I like to use a dab lithium grease for the ink disc post and collar, since that spins a lot during the run, and the grease doesn’t break down as fast as oil.
Refer to http://letterpresscommons.com/techniques/ Letterpress Commons for manuals, oiling diagrams, and great tips.
Have fun!