OP, I am in the middle of doing the process you describe right now. We lived in Hawaii until January, had previously lived in Northern California until 6 years ago. I applied for jobs in California for over a year after completing my graduate degree, finally got a great one last month.
We own a home here about 10 minutes from where the job I got is, had bought it in 2008 with the intention of living in it eventually and renting it out in the meantime. However, now that we're here we would like to buy a home, and leave the tenants in the house we own since they're paying substantially more than the mortgage, and we have the down payment available to buy a smaller house that we could live in for a few years and save some money until these tenants decide to move on their own. Currently I'm staying with friends while looking for homes and DH is wrapping up life in Hawaii.
The bank is fine approving us for a loan with my offer letter and new pay stubs, since I'm in the same industry I was in in my last state with equivalent pay (and I work for the government, which helps). It probably also helps that this bank bought the mortgage on the investment property we own and can see that it has been solvent. We are running into a bit of trouble with what they call "seasoning" the money for the down payment which means you have to have the money in your account for several months to prove its not a loan, and we are currently in the process of liquidating investment funds for the down payment and have to prove where all the money came from before we make an offer. (We can get prequalified, just not approved without seasoning the money.)
The other problem we are running into is that it is a very tight market for buyers right now. There's only one available home in our price range in our desired neighborhood, when 5 years ago we looked at over 60 to select the one we bought in our price range. Homes are going into contract with multiple offers within days of being listed, so if we see one we like we have to be prepared to see it and put an offer in on it, and I have yet to see one I like (have been looking in other neighborhoods, none are appealing). All this means its is unlikely I'll find something, and be able to close on it before my DH and DS get here in May. I had previously thought that 3.5 months would be enough time for me to get settled into my new job, find a home, and have it prepared for them. Since you're also coming from one of the non-contiguous states, know that just getting your stuff, acquiring/shipping the cars, re-doing insurance, etc, etc, etc, is exhausting and time-consuming all on its own.
So, we're resigning ourselves to the fact that we'll have to lose our great tenants

and move into the home we own

which we love and bought because we want to live in. We are working with a deadline though, since we want the DS to be in a certain school district we are familiar with since we lived in this area before he was born. Over the next year we'll keep hunting and probably buy another home as an investment property.
Between lending laws and the tight market and low interest rates, landing and buying a home is tough right now, especially when you come from far away. Not sure if my story will help you any, but perhaps it'll give you some insight into what you're trying to accomplish. Good luck!
If you want to get a house when you land, you'll need to have a job offer in hand, a substantial 'seasoned' down payment (offers with FHA loans are apparently not being accepted buy sellers right now since they have multiple offers in many places), and it will still probably take at least 1-2 months to close. Plan on being forced to rent for at least a month or two, possibly up to a year if you want to find the right house in the right neighborhood for you.