The screeching sound is almost always caused by a compressor that is cooked - where "cooked" is defined as: shedding parts into the system, and is seizing and needs to be replaced.
The other problem is that if the compressor has died, it's likely shed bits of metal into the system and that is going to need to be cleaned out. Usually this is done by using a solvent to flush out the system, thereby removing all of the lubricating oil which will have have to be replaced.
And to further complicate things, if you're going from an R12 system and 'upgrading' it to R134a, then you're going to have to change the valves on the compressor (or fit conversion valves) as well as replace the seals (rubber o-rings) that go between the various connections. (NB: that R12 is a better refrigerant but is very ozone unfriendly and is either banned or strictly controlled in most jurisdictions. Venting R12 into the atmosphere is punishable by quite severe fines if you're caught doing it. - plus it's quite valuable and you don't want to vent it in any case).
And, even a further note, that there are different lubricants used with different refrigerants and they are NOT cross compatible... you can NOT mix the various types. There are PAG, Ester, Mineral etc... Do some research and fit what is going to work with your system and your refrigerant.
And to make matters even more interesting, you might want to get into the system and test the various connections, switches etc. before you go to the (expensive) trouble of piecing it back into working condition again. The main failure points (other than places that will leak - hoses, connections, condenser, evaporator), are the pressure switch (88645‑12020) and the thermal expansion valve (88515‑87004) may become blocked or fail.
The filter/dryer (88470‑14010, Napa Canada NTC A7988) is going to need to be replaced as well, you'd better line one of those up. They are often a part that is used a across a manufacturer's line of vehicles and are not hard to get and not too expensive.
If you're unfamiliar with A/C, you might want to do some reading, do the wrenching yourself, then take it to a shop that is very familiar with A/C to get the system leak tested and drawn down to by vacuum to test its integrity.
Once it's leak tested, vacuum checked, and ready to go - make sure you have installed the correct amount of oil and refrigerant and it should work perfectly.
Hope this helps a bit.
~John
PS: part numbers are for a 1989 BJ70