I just put a Vintage air Mini Compact unit in my '37. It blows 38 degree air even on the hottest days. It will freeze up if it's humid out, but I heard before purchasing it they could do that. I am really happy with it, but it was expensive, not quite $1300 with everything needed to finish the job.
Best advise I can give is get the cooling system working correctly before adding air, fan shroud and good radiator. If you can't move the heat out of the condenser and radiator, it doesn't matter what A/C system you buy, it won't cool! I have a 18" mechanical fan with no clutch on a 250 inline with a 17" wide radiator just to be sure it stays cool.