Since 134A is the only legal freon you can get today, you need to upgrade to the system that willl run on it. As far as the system, the best compressor is the Sanden, and a few companies carry kits for that conversion. One is ClassicAir, and the other is VintageAir. Do some research with those two companies. If you have any wrenching skills at all, you can install the system yourself, and have an aircon company flush and install the freon.
Now, you can keep that old York compressor and have it converted to the R134A system, but it is most likely on it's last leg, so I would recommend replacing the entire system with new parts if you can afford it, otherwise you will just be throwing good money after bad. The average labor cost of replacing the compressor that you have bought and recharging the system is about 375 bux.