There is a 3rd type of compressor pump to be aware of. Sears and some other DIY type stores sell what appear to be a traditional belt driven piston type compressor. The difference is that they use a sealed bearing on the crank end of the piston rod, and do not have a sealed crankcase full of oil.
They are quieter than the diapraghm type, and seem to work well and supply plenty of PSI for our use. The problem is that when using them on a project that requires the compressor to run fairly frequently ( like shooting primer with a traditional siphon gun, or running a DA sander) the compressor overheats, the piston / cylinder get hot ( no oil bath to help cool the piston) and the piston starts seizing in the cylinder bore.
This causes the rod to break from the load, and sometimes wipes out the entire compressor pump. The replacement parts are / were readily available and easy to replace. I rebuit mine 2 times, then gave up and got a 5hp / 60 gallon vertical tank unit. It is a copy of an Ingersol Rand commercal unit, marketed under the Coleman brand and named the " Black Max" series. Any similar style will work and last lots longer than the "Oilless piston type". Harbor Freight sell some in this category that are ok for home / shop use and pretty affordable.
Check Craigslist and the want ads in your area, some really good units are 20-30 years old and look like crap, i.e dusty, grimy, covered with paint overspray etc. Some are junk but if they are name brand like Ingersoll Rand or Campbell Hausfield, they will probably still have plenty life left if they have been maintained at all.
On used compressors the things to check are :
1. Tank drain valve / tank condition.
If drain valve is free and you can open / close it easily that is an indication that the tank was drained on a fairly regular basis. If you open it and some stained / rusty lokking water runs out - that doesn't mean it is junk- just look it over extra carefully. If it is stuck closed with rust, won't open, or opens and won't drain- then there may be deteriotaion due to water collection / rust inside the tank. Be wary - a rusted tank could rupture - bad news.
2. Compressor - Check the oil, it should be close to full, and look fairly decent. Darkening / black can still be O.K. Milky white, rusty, or thick /gummy / stinky indicates lack of maintenance. Turn it over by hand and rock the pulley in / out, side to side to check for excessive wear / play. Also look to see if the seals are leaking oil.
3. Motor / belt / switch /. Motor should not looked overheated or smell burnt. Belts are often dry rotted / cracked. Pressure switch / on-off (usually a box mounted near motor with a lever, relief valve, motor wires running to it) should move easily and stay in position when changed from on to off.
If it looks OK - power it up and listen to it run, should not knock or clank, have excessive vibration, or leak air all over the place. You don't have to take the tank to full pressure, let it build to 50 PSI or so and shut it down. Listen for leaks at fittings etc. Start it back up to make sure the motor will start under a load and not trip breakers or built in over current / temp switches in the motor.
I could go on but you should get the general idea, lots like buying a used car or piece of equipment. Deals are out there- but you have to do a bit of work to make sure you don't get burned.