Yes, W-9 is the correct form. Apparently, you are being hired as a contractor, and not as an employee. Therefore all income earned from this will be considered self-employment income - meaning that in addition to the "regular" income tax you pay, you will also pay an additional 15.3% self-employment tax on the amount paid that exceeds $433. Read the references posted by Critter-3 so you don't end up having to deal with the hassles of tax underpayment penalties and a bunch of other stuff because you didn't make quarterly tax payments.
Also, for whatever you "home" state is, if they tax personal income you need to check their website to see if you're liable for paying state tax also, even though you may not be claiming your home state as your resident state. Most likely, you're not. But you need to confirm it beyond all doubt so you're not blind-sided a year or two down the road.
