I haven’t gone over what I use to make the sourdough. Most of it was already on hand just because we cook stuff, but there were a few specialty (read “expensive”) items that aren’t really needed…
One piece of gear you will absolutely need is a kitchen scale that reads in grams up to 10 kilograms or so. Weighing ingredients is much easier than trying to measure by volume. Another smaller scale that reads in tenths or hundredths of a gram is also helpful for weighing salt ( and occasionally, yeast).
I keep and grow my starter in pint canning jars. (Actually, I’ve found that a particular brand of pizza sauce comes in a perfectly-sized jar that oh-so-handily mates with canning lids.) I keep three jars – one for the current culture of sourdough, another for the next culture (daughter, if you will), and a third to grow a batch of starter to make a leaven. 
Hopefully a large bowl is obvious. I use a smaller bowl to make the leaven. I have a couple of plastic shower caps that came from (I think) Caesar’s Palace in Las Vegas that I use to cover the bowls between steps. Plastic wrap works.
 There’s an engineering method called the “Rubber Duck Technique”, which posits that if you can explain what you’re making to a rubber duck, then you fully understand what you’re doing. In explaining my need for three jars to you (as proxy for the rubber duck), I realized that I really only need two jars.