food

You can make it even more simply if you are willing to accept a certain margin of error too.

Shelf-stable apple juice is already pasteurized, so you can get a big bottle (maybe half a gallon or a gallon), crack it open and dissolve some table sugar with some juice in a clean jug (replace the lid on the juice immediately after pouring it out), add the yeast (use a champagne yeast if it's for cider - I've used EC-1118 but you are probably gonna find Red Star Champagne yeast in your region more easily than EC-1118), then pour that back into your bottle.

Airlocks are as simple or as complicated as you want to make them. The ol' balloon trick works just fine, especially if it's your first attempt but you can also use a proper airlock.

As a very rough guide, 1g of sugar per liter produces about 0.5% ABV so do some napkin math (don't forget to include the sugar already existing in the apple juice!) and make a target for your ideal ABV for a cider. Champagne yeasts can usually be pushed to near 20% ABV but that's overkill and it will end up tasting bad. Also 20% ABV cider is gonna be a bit over the top. Aim for around 4 to 8% depending on what you're looking for.

Do not rely on this ABV calculation as being anything more than a rough guide, do not drive if you're gonna drink this cider unless you've actually measured the ABV!!

After priming, your cider will be very dry but it's easy to make a simple sugar syrup or sweetener syrup to back-sweeten a cider directly before serving, and you can customize your sweetness to taste individually this way too. It's just a little frowned upon for some reason because I guess it feels a little too close to being a cocktail or something? Idk, don't ask me - sweetening in a bottle or sweetening in a serving glass doesn't seem all that different to me.

Last tip is that malic acid can really elevate even the most basic cider, especially if you like depth and sour notes. Be very sparing with it - it's extremely concentrated.

Honestly you could make the Apfelwein, put some aside to prime into a strong cider when bottling, and play around with it to see what you like. (Just make sure you do your research before you try priming since bottles become bombs very easily if you are careless and the cleanup is fucking dreadful, aside from the obvious dangers of glass fragments exploding around you.) The yeast will cost a few dollars and so will malic acid, if you opt for that, but as a project you can probably make half a gallon or a gallon for less than $10 all up.