I try to keep it simple, but that does not mean "Simple Green". That stuff is almost useless unless you jump through a series of hoops including tumbling and forced air drying. Personally, I use trichloroethane or "Ensolve". These chemicals will cut silicone grease or oil like nothing you've ever seen. Won't rust the tank and leaves no residue. A handful of greasy valve parts dumped into trichlor is O2 clean in 10 seconds. Same for O rings but be careful with plastics.
I've read all the posts and find them very well informed. The bit about distillation of gases was interesting but don't get hung up on variations of O2 content from compressors, doesn't happen. There are some concerns, mostly minor, concerning CO. Long ago, this was a problem with old war surplus two stage GE compressors creating a diesel cycle through overheating and combustion of the lubrication oil. Modern hp compressors using synthetic oils don't produce CO. There remains a problem, potentially, with portable compressors sucking exhaust gas. (position the exhaust downwind and use a long intake tube). The real source of CO, as one poster pointed out, is auto exhaust gas. I don't see how city people can get clean intake air and so a catalytic filter element should be installed on compressors located in metro areas. These are widely available. Doesn't hurt to ask the shop if his filter stack includes "hopcalite". If he knows what that is, you are probably OK. Some will display an air assay report.
Grade E air is theoretically not pure enough for use in an oxygen clean tank. Over a period of time and many fills, minute amounts of oil can accumulate inside the tank to create a problem should it be subsequently charged with O2. The compressor should have an extra "fine" filter to be safe.