Although i am not a tech, I just went through this process on my '87. When mine started running cool instead of cold, the Tech added dye to the r-12 system and had me bring it back after using it for a week. This isolated the leak(s) that needed fixing no matter which R coolant you use. He then captured the r-12, fixed the leaks (fortunately just 2 bad 'O' rings), replaced the receiver/drier and expansion valve, and evacuated the system for most of the day before adding the R-134A. A/C conversion
Cost for my system was under $400. Depending on where your leak is, your conversion could be more, even a lot more, especially if the evaporator, condensor, and/or compressor are involved. Wherever the leak (preferably found with the dye method), the minimum that needs to be replaced during the conversion are the receiver - drier and the expansion valve, and the system should be evacuated for at least a couple of hours.
This is pretty much what i remember from my conversion. There are several good threads on the conversion in the archives as well. My experience with the r134 is that it seems to take a bit longer to get cold, but seems to chill just about as well as the R-12.