Do I send my thank you letter to each person individually? Or do I pic
and choose? Or should I email them all with one email? Or perhaps I
should do something else?
Yes, send your thanks to everyone you met.
Use customized individual letters (or customized individual emails, if you prefer).
The point of a thank you letter is usually to get yourself a bit more attention from the hiring company. Thanking everyone individually gives you a chance to highlight something discussed with that individual, and hopefully make an even better impression.
Think of something, some special connection, that you can convey to each individual separately. Show them that you are willing to put some effort into things, rather than just tossing off a "Thanks" email and copying everyone. A good job is worth some effort.
You never know which individual might put in a good word that is the tipping point leading to your hire - thank them all, and make it feel personal.