Izotope Vinyl is good for lofi record sounds.
Best bet for an old broadcast is to add static/radio noise as a seperate track mixed at a level that you find optimum. I'd low pass filter the white noise at about 800khz though, then just add some radio modulation noises or make some using any of a half dozen freeware AM (amplitude modulation) style plugins. Ring modulators may work as well, but AM can produce sidebands that add authenticity to the sound.
Next thing I'd do is hard compress the crap out of the summed audio (commentary, any produced sound fx, static and radio 'noises') to give it that old time radio zero bandwidth feeling, plus cheap limited speakers. Then I'd spike EQ around 1khz and 3khz to get it trebly and nasty.
Then run a bandpass filter from 600hz to about 3khz to get rid of the high end and low end. Lose more lowend than high, but you want to make it sound super lofi.
The imperfections will 'sell' the audio. Listen to 30's broadcasts for the types of overall sound, imperfections, glitches and sounds present. Aim for authenticity and you can make it very believable.
Any music they play on air should be heavily processed with Izotope Vinyl in the 1930's setting, with some dust and electronic noise added into it. Make the source music sound real as well--that it came off an old record player and THEN got further mangled by being broadcast.
Don't forget to slap a limiter on the audio as well, to simulate the limiters used in radio broadcasts.
Good luck, I hope this helps.