Reddit reviews The Complete Book of Pickling: 250 Recipes for Pickling, Fermentation and More

Denmark's Ribe center has resources for period foods including cheese (fermentation of milk for preservation and taste) and smoked meat and fish (which, while this is not fermentation, it is preservation). Bread, especially sourdough, is also a form of fermentation and so, obviously, are traditional alcohols (beer, mead, fruit wines). Here's another resource with period recipes.

Look toward modern fermented fish recipes—they likely have not changed much. Asia continues to have a vibrant culture (HAR) of fermentation but fermentation is a Thing that most cultures developed—yeast, after all, one of the main requirements for fermentation, is in the air just about everywhere.

You asked for "something similar but more close to home". What is "home" (do you mean ancestrally or currently)? It's very likely that you can find a local pickling group that can help you learn how to pickle things and, once you've pickled one thing, you can pickle just about anything. You can also hit up Amazon for pickling.

Or, y'know, ask your elders, especially the women. Most people who are in their 80s–90s now pickled. Most people in their 60s–70s learned to pickle from them. This is due to WWII and is pretty much going to be true regardless of country.

If "close to home" means "my family is from [Germany/England/Sweden] but I live in [France/South Africa/Mexico]", a solid google search in the language in question should lead you to local modern recipes. For the most part, pickling has only changed with regard to the technology not with regard to the recipes.

Share what you make! Remember that your dísr are at your elbow as you ferment! Honor them and ask for their luck in your success.

Personally, I'd keep it simple... beets hold their own and don't need the extra spices. Classic Pickled Beet Slices from The Complete Book of Pickling.

If you're only doing a couple jars, just skip the canning steps and keep them in your fridge.