Welcome to Chat! That is a very nice looking car. I know you will enjoy it.
You can start your research at the site linked below. Many of us on the VCCA Chat have put together a collection of literature related to the cars we own. It is very important.
Old Online Chevy Manuals Even if you do not plan to do the work yourself the reference material will help a competent mechanic do it properly.
With respect to adjusting the brakes (which I agree is the second task I would try) you can use the information in the 1938 shop manual on that website. The brake design and service procedures did not change between 1938 and 1939.
Adjusting the brakes is not a difficult task but does take time and attention to detail. You need to equally adjust each shoe in each brake. The one issue you might encounter is whether the adjuster mechanism is stuck. One tip I have is to remove one of the rear wheels and the brake drum. Then you can look at the brake mechanism and understand how the adjuster works.
The first task is to make sure there is adequate brake fluid in the Master Cylinder. There probably is but I always start with that check.
