If you have not done any kind of restoration/conservation work, just clean it up and leave it alone, use it and enjoy it as found. It is more valuable and desirable to a serious collector in that condition showing its age and patina than refinished. If it is from the 1930s and was used, it should have the marks and distressing of an almost 80+ year old furniture. No refinisher can replicate that.
The least intrusive type of cleaning like light dusting/vacuuming then just wipe with a damp cloth with a mild soap on a regular basis, avoid using oils or anything with chemicals that could affect or remove the existing finish. There are books in the public library (if you have one in your area) that you could probably check out and read up on how to maintain valuable antiques/furniture.
If this has structural issues, try to fix it just like how it was put in originally, don't try to improve it if you can avoid it. The image looks like it is in very good shape though.
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