Generally my order of choice for solvents is water, IPA, acetone, methanol. Water is too often overlooked. If water won't damage your device, it is usually the best thing to start with. It is very polar, so it dissolves a lot of things the organic solvents are not so good at. If you use DI water and have no pockets that can trap water, it is ok to let it air dry. Gentle heating will speed the process. Otherwise, follow with IPA and blow off with compressed air. This will do a pretty good job of displacing the water so it doesn't leave its dissolved salts on the board. Acetone is the heavy duty basic solvent, but is the most likely to damage your device. Methanol is the most heavy duty alcohol, and is good to use when IPA isn't strong enough and you can't use acetone. Both methanol and acetone evaporate very quickly, which can be annoying -- if it evaporates too fast it will just redeposit the crud it dissolved. I don't usually use ethanol because it can be hard to find pure.
Mixed solvent cocktails like paint thinners and grease removers can be very effective, but they are not very clean themselves. You may need to follow with water and/or alcohol to get a really clean surface. Another factor here is that lots of devices specify solvent resistance for alcohols and acetone, so you can be more confident it won't do any damage. Other solvents may be more of a gamble.