Hey StrayDuck230!
I also have a '37 Chevy project, but mine's a pickup. At the rate mine moves forward, you'll probably beat me to a car show (show and shine, whatever!) and I've already invested about 13 low-intensity years. What 327 nut says is largely true. Your '37 did originally come with "juice" brakes, but the system is old, tired, long-stored and probably in need of replacement. Seriously consider a dual braking system (two reservoirs, so at least some of the brakes work if there is a catastrophy). I also recommend you consider disk brakes, at least up front.
I think there were two different suspensions on the passenger cars, one (I think) was the straight axle, similar to my truck, and I think the other was a sort of independant suspension (called knee action, I think). Seems like the knee action was on the Master models, and the beam on the standard. I suppose either will still work, if put into good condition, but I don't think either was really very good. Just a head's up here.
Lastly, Chevs of the 40's, and others, sell lots of parts, most of them new, a few off their parts vehicles. But those new parts (for 37s in particular) are largely made by a company called I & I reproduction parts. They are in Paramount, CA. I think they sell to the public for near what they sell to the retailers for. You might want to check their web page, and get a catalog. Good luck on your new project, and call on us for help whenever you need it. There is an amazing amount of knowledge here, as I am certain you will learn.
Pat