Jeff,
There are almost as many ways to solve your problem as people here on the Forum. Let me tell you what I would do. Please remember I am a die hard do it yourselfer.
First, get your hands on an evacuation pump. If you can't find one, it is easy to make one. Find an old compressor from a deep freeze or household fridge unit. Wire in a switch and solder a pair of R-134 connectors on the ends of the lines. Get a set of 134 gauges/manifold set.
Now, try if at all possible to find the jobber source in your town that supplies a/c parts to the local repair shops. Most the time if you pay cash you can pick up high quality replacement parts a little cheaper than at the local retail outlet. If you are a purist, go to the Chevy dealer or through a vender on this site and get original equipment.
Most of the compressors you will buy as a replacement can use either R12 or 134 A. You will be buying a direct replacement for the 84 compressor that is already on the car. You need to get a handful of o-rings from the store, Ester Oil, receiver dryer, orphis tube, and flush fluid. Take your system apart and flush the evaporator and condensor. Either buy new replacement hoses, or have the A/C shop put new rubber on your old lines.
Oil the o-rings and snug up all the connections. Install the new compressor with the appropriate amount of oil in it and the dryer unit.
You can now hook your homemade evacuation pump to the car on the low side (shrader valve on the dryer unit) and allow it to pump for an hour or so. Longer if you have the time. You will see your manifold gauge go negative to around -30. Shut the pump off and watch the gauge for a couple of hours, or even overnight. Make sure it stays in the negative spot. That means you have no leaks. If it keeps going back to zero you need to recheck all the connections.
Finally, when it is holding a good vacuum, you will be able to shoot at least one can in with the engine off. When you can no longer get the can of 134 to empty, hot wire the low pressure switch on the dryer back to itself and start the car with th a/c on. Now the system will be forced to pump and pull in the remaining amount of freon. The 134 works under a little different pressure than the R12. I usually run about 80% of the R-12 charge to get it right. Ask the local supply shop for their suggestions here. There is also a little known adjustment screw in the middle of the low pressure switch. You may have to back off a turn or two to get the compressor to cycle correctly. Ask the supply shop for their suggestion here. It will all depend on the pressure you have on the low side. Usually the stock setting is fine. However, if it cycles to often just back off a turn or two. I would consider replacing the switch all together. They are farily cheap and can be a source for leaks if still the original equipment.
You may notice at slow speeds and heavy traffic that the 134 is not as cold as the R12. If this is the case, put an additional pusher fan (if not already equiped) on the car to help it cool.
Finally, you will screw on the 134 adapters of course when hooking up the manifold set to the car. Now you are fully converted and will be able to service it yourself in the future if you develop any leaks.
You should end up around $200 to $300 in materials depending on how much you pay for a compressor. The replacement hoses will add more, from either about $75 to $250. Do not be tempted to run the old hoses. Even if they look good on the outside. The pump may be free if you can find a discarded unit or pick one up from a local utiliy repair shop. A do it youself quality set of gauges will run around $125.
If you have never done a/c work before, I think you will really enjoy the satisfaction of accomplishing this project. You will become the envy of the neighborhood on hot summer days. Especially when you see what a good qualified shop gets to do this job.
Again, in reference to your question on parts or upgrade. The 134A Freon is the best upgrade. The best compressor to get is a brand new one from Chevrolet that is an exact replacement of yours. A rebuilt unit will cost a little less--it all depends on your budget. I personally don't think it would be worth changing all of your mounting brackets and belt system to go with a different style. I have converted plenty of the ones like you have with ZERO problems. I have even gotten lucky on a couple of old ones where I simply switched to 134. They do have a tendency to make a lot of noise.
have fun, be cool.