Wow. I don't think you know what you are letting yourself into. Phase change cooling requires a bit more research than I think you've put into this (so far). Believe me, I'm going to do my best, but what you really seem to need is a crash course on phase change cooling in general and HVAC repair in particular.
Let's start with the first problem. How can anyone help you if you don't say what the model number is for your compressor? Second, I doubt it's double loop. You might have two extra tubes (one on inlet and one on outlet) for monitoring and fill points. Someone else (hopefully) knows more about that than I do. But, the best place to get info on your compressor is from the manufacturer.
Second, did you know that the oily fluid you drained out was supposed to be there? It might be POE or it might be mineral oil depending upon whether the compressor was designed for newer (non-CFC) gases or if it was designed for the good old R-12 or R-22 style gases. If you decide to go with propane, you should use mineral oil, and if you go with R-134a, you should use a POE type lubricant. Did you know that you have to clean out your compressor if it was using the other lubricant? Did you know that compressors are designed for one particular gas (they might be able to use others at a reduced efficiency though)?
Do you know how to calculate the required cap tube size? Do you have a set of gauges? If they've ever been used with R-12 systems, make sure you don't use them in a newer system like R-134a because of the minute presence of mineral oil which can damage newer systems.
Preventing "stagnation" is important, true. However, the primary problem is the LUBRICANT, not the refrigerant. If you don't get the lubricant (which is dissolved in the refrigerant) back to the compressor, you can expect a smoking compressor real soon. Basically, use common sense. Depend upon the fact that liquids fall "faster" than gasses, and that the lubricant will move best with gravity instead of against it. Look at typical refrigerator/freezer designs. Do they have the compressed gas going into the TOP of the condensor or the bottom? After the phase change is complete, don't worry. Everything will get pushed. It's where the phase changes happen that you need to worry. Look up things like "accumulator bulb" and "flooded evaporator" using your favorite search engine.
I recommend propane because of it's cost per unit of performance. Unless you have a source for the more exotic refrigerants, it's hard to beat propane. Some people are concerned because propane is flammable, but just be careful. You'll only be using 2-6 ounces anyway (unless you have a really large or just badly designed system).
Yes, you'll need a vacuum pump. If you leave water in the system (by not evacuating it), you will be very likely to burn up your system. Water has a habit of eating up compressors because it interacts with the lubricants and the refrigerant to form hydrofloric acid. Also, even if you don't think it will get that cold, water can very easily plug up your capillary tube.
How do you control your compressor? Use a thermocouple to sense temp, and make it bistable so that it comes on at a higher temp than it turns off (otherwise it will flutter around the turnon/turnoff temp).
Have you read the ProCooling article on phase change? Please do
here. It has a lot of basic theory that should help ya.