The old R12 systems used mineral oil. The newer systems (all cars since 1993 or 1994) using R134A use either PAG or POE oil. POE oil is used mostly for retrofits of R12 systems to R134A. Volvo specifies PAG oil. I am aware of no "special" PAG oils and they are sold under various brands. There are 3 viscosities of PAG oil. The highest one is used only in GM cars based on the label I found on a can of it. The choice of medium or low viscosity depends on the particular compressor (a list appears on some cans of oil also). You may be able to identify the compressor manufacturer and type by its label. Sanden and others have web sites with specifications. I used medium viscosity PAG oil in my system.

The hard question about oil is how much you need to add when recharging. Oil accumulates in the evaporator, compressor, accumulator and condenser and is circulated by the refrigerant. If any part has been replaced as much oil needs to be added as would have sat in that part.

When recharging an empty system (not opened up) I put in one can of R134A without oil and one can with it to cover possible losses of oil via the leak. After opening the system and replacing my evap and accumulator I added in total 4 oz of oil to cover approximately the amount that I was able to pour out of each unit.

Only 2 types of oil...(can't recall the exact names)...one that is for R-12 systems that have been converted and then the second type is the oil that is for the 134-A systems. Volvo always comes up "with their own" and charge an arm and a leg. You'll be okay with the stuff from Target...that's what I use and have had no issues.
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1998 S70 T5 Emarald Green Metallic, 2004 V70 2.5T Ruby Red, Previous Owner of Black '94 850 Turbo Wagon