As I'm brand new to this, I thought the best way to learn would be to start with the songs I hear every week. But, since it's obvious they don't write sheet music for theremini, what do I even look for?
Well I can't speak to any of the Theremini-specific stuff, but from a musical standpoint starting with the (simple) temple songs you already have burned into your ears certainly seems reasonable.
You probably want to start with the very basics (http://www.thereminworld.com/Learn-to-Play right here has some good resources) and get to the point where you can do one or two octave scales reliably first so you have the notes and positions "programmed" in your hands, but then you should be able to pick out the simple melodies from Shabbat music you know.
If having the sheet music helps then they certainly write sheet music "for Theremin" - It's the same as sheet music for voice (or any other monophonic instrument you like - flute, oboe, saxophone, etc.) and I'm sure you can find at least the vocal melodies for Shabbat music online somewhere. The tough part is translating the notes in sheet music to hand motion/positions. (I'm a string player myself so that analogy is natural, I think the equivalent for a trumpet would be translating the notes to the changes in embouchure you need to get the desired pitch?)
As a side note there are apparently "graphical notation" systems for Theremin. I'm not really familiar with any of them and there doesn't seem to be a consensus or standard, but there are probably some posts on here that talk about them. I expect that since you've got experience reading sheet music you'd probably find it easier to build on that than learn an entirely new system of notation though, and long-term it will probably be easier to learn new pieces off "regular" scores than have to re-score everything yourself.
