If you have access to an air compressor that really helps in blowing the debris off (use it outside!). Using a paintbrush will help too, and if you don't have a compressor it can also do a decent job of initial cleaning. I like to blow, brush, and/or scrape (plastic putty knife) off as much as possible before wetting the chassis with chemicals.
Chemically I usually start off fairly mild with something like Windex, 409, or rubbing alcohol (get it cheap at the drug store)........ sometimes even a damp rag will be all that's needed. I start out mild and then work my way up if required. There were a lot of good suggestions tossed out here so I won't rehash them, but I will say be careful. Read the directions for any warnings and to make sure it doesn't need to be rinsed off. For rust, and even some tough cleaning, Naval Jelly works pretty well. It does require a rinse so at least go over it a few times with damp rags. Buying a box of
nitrile or latex gloves is a good investment.