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Looks like it only needs is a good wash job. I don't know much about the '39 though. NICE car!!
Jim
My area of expertise is more in the '50s, but I think I can help a bit.
It appears that you have a business coupe, though I am not familiar enough with the details of the '39 to know whether it's a Custom or DeLuxe model and unfortunately I don't think you can determine that by the serial number like most years: https://desoto.org/community/general-discussion/custom-vs-deluxe/ The best I can find for identification without locating a brochure is that the Custom had a darker interior than the DeLuxe.
I assume you have checked out this page? https://www.desoto.org/1939-2 We need to get the Windsor (Canada) serial numbers added, so if you don't see yours listed here, that could be why. I believe the serial number is located in the door jamb.
What I did notice is that the headlights are not the unique one-year-only oval shape that I am accustomed to in 1939. It kind of looks more like the 1941 headlight design. It looks like the car is in really good shape and I love the color. If you recently purchased this, I'd say it is a good buy based on the photos!
I'd encourage you to send in the form to obtain a FREE copy of your car's build card from Chrysler Historical, which will give you more codes and they also can tell you the original selling dealer in most cases. The form and instructions are located here: https://www.desoto.org/historical
I hope you'll also consider joining the actual club as you'll be connected with additional resources, such as technical advisors, access to the club library for references, free classified advertising, and connecting with other '39 owners through the club's annual roster. https://www.desoto.org/membership
@AlSmith might be able to help more as he owns a '39 and is quite knowledgeable.