In a production environment, printed circuit boards are cleaned in what basically amounts to a dishwasher. Before the CFC ban, tetrachloroethylene was the cleaning solvent of choice, but now most factories use water soluble fluxes and clean with water. The final stage is a rinse in de-ionized water so you don't get mineral deposits that can alter the circuit performance. Spot cleaning now is usually done with denatured alcohol.
Use metal pans, and don't wear rubber shoes, to avoid electrostatic discharge. Non-distilled water is conductive, so I wouldn't worry about static from a wet plastic brush. If you are paranoid, add a pinch of salt to your wash water (to make it more conductive), and don't scrub during the final rinse in distilled water. You may want to consider dropping a few coins for an anti-ESD brush from the Techni-Tool catalog or similar outfit, especially if you have to scrub a lot with alcohol.
https://webvia.techni-tool.com/VIA/Res/Catalog110/178_TTL_Cat110.p1.pdfWithout a bake cycle, it will take a couple of days for the water to dry out from all the nooks & crannies under the chips. Or maybe 12 hours in front of a fan, but make sure all the surfaces are exposed to moving air. You don't want to power her up when the board is wet!
It sounds like you have a lot of stuff, so you may want to let your dishwasher take up some of the work, though I would go easy on the detergent (maybe 1/4 of what you would use for dishes), and turn off the drying cycle. Then spot clean with alcohol as necessary and final rinse in distilled water. I don't think the A500 or A1200 have any non-cleanable components...you don't want to wash the lubricating grease out of a switch for example.
Oh, and the keys. Pop them off the keyboard, put them in a mesh bag, and drop them in the clothes washer with your next load of cold water. Though some people have reported success putting keyboards in dishwashers, I cannot say if an *Amiga* keyboard doesn't have grease in the mechanism or places where water will be trapped indefinitely.
