I was in TS Boston 2010 with Loudcaster.
You get in by applying. I would apply early and send TS regular updates regarding the progress of your project since applying.
I have my own opinions about which model is better, but if you are willing to move to be in a business acceleration program for three months, then you should apply to both.
I think I recall some TS staff suggesting people apply to both, otherwise you're limiting your options, and you're in a great spot if they both want you.
You'll get the optimal experience by dividing and conquering. You're supposed to come out of it with a better business sense and a product.
You need to find the right balance between product development and business development, and having the right partners is key to that.
Whoever is the CEO for all intents and purposes should probably go most of the sessions, but not the whole team. This can be a little tough if the CEO is also one of the coders, so it's extra handy if your partner is also a coder.
You should also be very proactive going through the mentor list and reaching out to mentors early.
Oh...and when you get accepted, grab your office early and get the one closest to the entrance because a lot of mentors will drop in the first couple weeks to meet everyone ;)