Disclaimer:  Fermenting food at home is considered very safe and has been done for hundreds of years (if not longer) to preserve seasonal food for eating throughout the year. I am not a food scientist, nor do I play one on TV, so before you jump into fermenting food at home, please do your own research to make sure you're following safe practices.  I've included a link below to a very thorough site that describes how to safely ferment food at home if you decide to start down the fermented food rabbit hole:

https://www.foodsafetynews.com/2014/03/fermenting-veggies-at-home-follow-food-safety-abcs/

Compared to my other fermentation hobbies, fermented food (at least to start) doesn't require that much equipment besides what I already had in the house.  I'm sure this can grow depending on the type of food you're fermenting or the process you're following, but the basic setup is pretty simple.

Wide-Mouth Mason Jars, Lids & Rings

I would suggest starting with pint or quart mason jars and move up in size from there as you find recipes you like or if you're planning on sharing with friends.  You can find them on Amazon, but they will most likely be cheaper at your local home store.

Fermentation Lids & Weights

I tried some naturally fermented pickles a few years ago, but the process had me releasing pressure from the jar a couple times a day under threat of the jar exploding.  Needless to say, I wasn't a fan of that, so I didn't try another batch until recently.  After doing a little more research, I found a lot of people use special lids that allow CO2 to escape during active fermentation.  I also learned that you really don't want your vegetables sitting above the brine, or you risk mold developing and ruining your whole batch.  To remove/reduce this risk, they make glass fermentation weights that sit on top of your veggies to keep them safely below the surface of the brine.

Water Filter, Measuring Cup & Thermometer

Most municipal water supplies contains chlorine, which can inhibit/prevent natural fermentation form occurring.  I use filtered water from my fridge that I heat up to around 90 degrees in the microwave in a pyrex measuring cup so I can dissolve the salt in the brine, but not be too hot to kill off any naturally occurring yeast & healthy bacteria.  You can play around with using store-bought spring or distilled water if you'd like to try some experiments and see what works best for you.

Kombucha

Not technically a "food" I suppose, but I fermented a couple batches of Kombucha a few years ago.  It proved to be a bit too acidic for my acid reflux issues, so I ended up giving my equipment to a friend to enjoy.  Kombucha is super easy to brew and you can keep a batch rocking in the fridge with the equipment in the links I listed at the top of the page.  Give it a try and see what you think!

Standard Natural Fermentation Process

You can ferment just about any vegetable by washing it, cutting it up, putting it in a clean jar, and adding a simple brine to cover.  A standard brine recipe is 1.25 - 1.5 tsp of salt per cup of warm filtered water.  You want to make sure that your water doesn't get much above 90 degrees, as the lactic acid bacteria and healthy yeast may be killed off if you go warmer than 110 or so.  If your water is a bit too hot, just let it cool at room temp for a bit or add an ice cube if it's very hot.  After you have your veggies covered in brine, add your fermentation weight and screw on your fermentation lid.  Most recipes suggest leaving the jar at room temperature for 3-7 days, but you can test after a few days to see if there is enough acidity for you.  After you reach your desired acidity, add a standard lid & ring, and put the jar in the fridge.  You may want to leave the lid on a little loose or check the pressure every few days, as I've found some batches tend to keep fermenting at the cooler temps, and you don't want the jar to explode inside your fridge.  That would be very bad!

Recipes

Google is your friend for recipes!  You can also join FB or other social media groups to see what other people are fermenting at home.  You can start out easy with just vegetables & hot sauce, or you could dive way in with sauerkraut, miso, and/or kimchi.  The fermentation world is your oyster, so pick what works for you and see what you come up with!

I was probably the most excited to try making my own fermented hot sauce after playing around with some peppers, carrots, and cauliflower.  After looking at a few recipes online, I decided to try out a red and a green fermented hot sauce to see how that worked out.  Overall, I liked the flavor of both sauces, but I need to get a better handle of how to season the sauce as I'm blending it together.  I may also try heating the sauce to pasteurize it next time potentially, and this would also allow me to potentially toast some spices to add in as well.

Green Hot Sauce:  Fresh peppers (bell, banana, jalapeno)

Red Hot Sauce:  Dried peppers (ancho, chipotle, guajillo)

Additional Ingredients:  Distilled water, white vinegar, salt, and other spices to taste

Process:

Ferment peppers using the standard fermentation process listed above.  Once the peppers are at your desired level of fermentation, strain the peppers, but be sure to reserve the fermentation liquid.  You can then add some of the fermentation liquid, white vinegar, distilled water (if needed), salt, and other spices to your personal tastes.  I didn't do a good job of keeping notes on these two batches of hot sauce, as I was trying to play around with flavors and see hot things turned out.  Next time around, I'll try to keep better notes.  Below are links to some hot sauce jars & funnels that I used to store the sauce along with the different dried peppers I used on my red sauce: