I spend a lot of time on moble a/c units and have never seen a weak compressor. They are either good or have self destructed. If the a/c had no charge when you carged it there is air in the system and it will have to be evacuated but most of the time when there is air in the system the a/c compressor will cycle due to low psi on low side and extremely high pressures on the high side. Your fan would also be on.
For a check get in your car after it has cooled down or overnight. when you get in and start it up turn your a/c system to high as well as the fan. The fan should kick on within 3-5 min depending on the outside air temp abouve 60F. Your high pressure switch on the a/c should kick the fan on well befor your car reaches operating temp.
I would jump 12v to the fan and make sure it turns on If it does not while doing the previouse test. Your comopressor will not make a difference on 134a. The difference was the compatability of oils in the systems. They have corrected that by using an oil with 134 that is compatable with the oil used in r12 systems. It runs at a relitively higher pressure than r-12 but the difference is the coil area due to r-134a not being as efficient at transporting heat. It will not be as cold as an r12 system but should be comfortable.
Does the car overheat without the a/c on???
Sorry for the random extra info. Needed a break from studying the human body.