I moved to the US last year and was in the same position. One good thing was that my company had relationships with local apartment complexes and so as a preferred employer in the area, I got a bit of a deal (no application fee, reduced 1st month rent) for my apartment. You may want to ask your company if they have established themselves in this way.
When I applied for my apartment (PA) they did a background check and verified I had a bank account (which I got the morning I applied). So I was accepted, along with my verification of employment from my preferred employer.
As for credit, I am one who is using the RBC Centura services. I have a Visa check card with them, and once the CDN dollar started soaring last year, I asked them about obtaining a US credit card. Since I had the RBC account in Canada and maintained a Canadian credit card, they used my Canadian credit hiustory to get me approved. The RBC Centura customer service people were very friendly (was actually a Canadian that I dealt with) and I got my Visa credit card very fast after applying and being accepted.
The other bonus with an RBC Centura account is that through web banking, you can
transfer money between countries and it is accessible right away. Prior to having a Centura account, I had to write a check to myself from my US bank and deposit into RBC account in Canada, who had a hold on the check for 15 business days. So this is a nice feature. I think TD might offer the same service, but I am only familiar with the RBC service.
Hope this helps.