Franky, Suniso 3GS is a naphthenic mineral oil, the standard lubricant used with CFC refrigerants. This oil will be difficult to move around the system with R-134a due to the poor solubility. Your particular application may work with 3GS, but you will need to test the oil return characteristics very carefully to prevent any issues with poor oil circulation. There are very few companies who have used mineral oils with HFCs, unless an oil return enhancer was added to the refrigerant (like propane or pentane). Adding a substantial amount of POE lubricant will also help circulate the mineral oil.
The most common lubricant used with hermetic recips using R-134a are POEs. There are two main types available, ones based on branched acids for better hydrolytic stability, and ones based on linear acids for better thermal stability and lubricity. The Japanese prefer the branched acid POEs while the Europeans and Americans prefer the linear POEs. The linear POEs are able to go to very low viscosities (<7 cSt at 40C) for good energy efficiency and still maintain lubricity.
Both products work in a well manufactured system.