One thing at a time.
# 1 - HOW TO MIKE
How you want your theremin to sound is a very individual thing. There is no "right" or "wrong". The first question you must ask yourself is:
Is the sound I want from my theremin in any way dependent upon my speaker and amp setup?
If the answer is YES, then you must mike your speaker acoustically the way many professional electric guitar players and pedal steel players do. Do not try to plug your instrument directly into a recording device or console because you will get a much harsher sound.
If you are making a video and you want to get anything resembling professional studio quality sound, do not record your instrument using the built-in microphone in your camera. You must record a separate audio track as you perform and, after it has been properly mixed, sync it to the video image either digitally or manually. Yeah.....I know......it's a hassle....I can hear the groans already...but GET OVER IT! We are electronic musicians and we will pay dearly for refusing to take on the challenge.
Many thereminists just want to PLUG IN AND PLAY, and resist thinking about all the ins & outs of recording engineering. That's fine as long as you have someone else in your corner who IS thinking about these things. Clara Rockmore's recordings were engineered by Bob Moog! I have heard many fine thereminists come off as rank amateurs because they have been poorly recorded, and their performances go unrecognized because, as skilled as they may be, they sound terrible.
As the late Bob Moog said in ELECTRONIC ODYSSEY, "The theremin is an electronic instrument, and it is entirely at home in the electronic environment." Do not hesitate to use whatever electronic peripheral you want in order to get your instrument to sound as close as possible to your ideal theremin sound - whatever that may be. The quality of the equipment you use is going to depend upon what you are prepared to spend. High end (i.e. EXPENSIVE) audio equipment will give you far better results than cheap FX pedals designed for use with guitars.
The microphone you use should also be of high quality if you want to capture the clarity and transparency of your sound. Don't even THINK about using that crappy little thing you bought at Radio Shack for your computer. If you are using a reasonably decent mike, you will need a power source for it.
My own mike setup consists of an Audio Technica AT4033 (about $400.00 new) which I plug into a MILLENNIA STT-1 preamp (about $3000.00 new). The preamp is then plugged into the recording device which is a whole 'nuthah topic.
O.K., O.K.....I understand that not everyone is going to be able to justify spending that kind of money on a mike and preamp, so don't get all huffy! TL Audio makes some great preamp equipment you can pick up for a few hundred bucks. Their Ivory Series 5051 is great.
A chain is only as strong as its weakest link, and that goes for your recording setup as well.