Tesla has a finance deal with Wells Fargo for the Model S and X, I assume they will continue to do the same for the 3 but of course you don't have to use the capitve lender. Penfed and DCU have the lowest interest rates around the vast majority of the time so it would be good to join one of both of them so you have plenty of options. I financed my M2 for 2.75% over 72 months with scores around 680 so a good rate is pretty easy to achieve right now. There are some analysts who say lending for cars will tighten up but I think that is for subprime so as long as you can get in the upper 600's or higher you should be good. Also remember that the 35k promise from Tesla is for the absolute base car, I would keep your budget open for some options because that 35k car may or may not have all that you want.
Good luck. I have a deposit down on a 3 but plan on entering a lease soon on a different car. Considering that the base is 35K I planned on spending about 60K all in. A friend drives an S and he loves it. But I'm in the market for a car a bit sooner than the 3 will be available to me (whenever that is).
Anyway, I hope you get the car you want, when you want it, at the price you want