The installation of a factory type (Philco) radio in a '37 is a pretty simple straight forward operation.
The radio consists of three parts, the receiver, dial head and speaker. The '37 dial head has a V8 in the center of the dial that acts as the station pointer, rotating as the dial knob is turned.
There are some portions of the installation that must be followed, suppression of external interference from the ignition, generator, and fuel gauge.
I have a factory installation brochure for the '36 Fords which should be the same for a '37.
It has been my experience that only the Delux models were pre-wired for the roof antenna, My '36, a late production Delux has shielded wire from the chicken wire in the top, and a leg down through the body for the a running board antenna.
A cowl mount antenna on the left side works very well on the early Fords. Hooked up correctly the roof antenna works great.
I put a radio in my brothers '37 4dr sedan for him many years ago. The cowl had the "dipples" for the mounting bolts..
It is not a good idea to hook up the power to the ignition switch. The early Ford V8 switches are very weak not likely high drain through them. If you try to play the radio with the key on and the engine not running, you will run the risk of frying the points.
Some of the '36-37 Philco radios I have seen have a toggle switch that mounts under the dash. Switch turns off the power to the radio so the radio can't be turned on by people that don't know what they are doing.