You will need to get your permit first and I assume you've checked out whether you're eligible for one. You or your company should do this before you move here because as a US citizen getting a residence permit is not a given. I am assuming that your new employer is up to speed on what is required.
If you have all the documentation then getting the permit is relatively simple and your company will probably be able to help with this.
You need to register at the commune you will be living in so you will need an address for this. If you are living in temp accomodation or a hotel when you first arrive this will be acceptable but you may have to deregister from that commune and reregister in the new commune once you find a place to live.
You'll need your residence permit to be able to change your drivers licence but that is pretty straightforward.
For finding a flat then there are plenty of wessites to check out homegate, immoscout24, anibis etc (I think there's a sticky with this info somewhere)
Kristanez (on here) has a nice light 1 bed appartment up for rent from December 1st but you'd have to compromise on the view. Search for Neuchâtel and appartment and I'm sure it will come up.
It shouldn't be too difficult to find a suitable car/van when you get here either.
Oh and welcome to Neuchatel it's a lovely place to live. You might just get here in time for the Christmas party.
Sorry I haven't provided better links but it's not so easy to do on my phone,