In small reciprocating air compressors 30 wt. non-detergent oil is all that is needed. I have found if the machine is kept outside you want to change it at least 2wice a year, inside once a year. Stuff labeled compressor oil is a selling trick, easy to charge a couple bucks extra to re-label a quart of oil. If the machine is new or recently rebuilt, run a mineral base (30 wt. non-detergent) for a couple of months then change to a synthetic and it will run cooler and longer. As far as a synthetic make sure it is a diester synthetic made for reciprocating compressors. This won't be that easy for usually this stuff is reserved for the large (50 hp. and up) compressors, nor is it cheap.
Whatever you do don't put a synthetic into an old machine that may have a carbon build-up on the inside of the unit. The synthetic will decarbonize the unit and the carbon will get into places you really don't want it and could damage the machine.
I have seen several times in GJ the mention of compressors detonating, in over 30 years I've never seen or heard of it. I've seen a 10" high pressure piston of a 2 stage compressor have a complete meltdown and molten aluminum be pumped in the head and valves. I've also seen line fires, where the piping in a plant have so much oil residue in the piping and the poor compressor maintenance cause a fire. All you can do there is close the piping and hope the plant doesn't catch on fire, then replace all the piping.
Oh, and I have seen the tank blow up because of rust thru, but not from oil building up and spontaneously combusting.
But anyways, 30 wt. non-detergent should do you just fine. The discharge pipe should be over 200 degrees.