I too would start at 10k or more Cheryl. With 3k, your already broke
Start with your moving expenses over -flights etc. Your hotel expense until you find a home/apartment. Rental car if you choose to sell your truck in Texas ( more on that later) , your rental home deposit and first months rent. Utility deposits/ fees/connections.Weekly food/gas /any monthly bills you would be bringing with you like credit cards. Car insurance/health insurance. When you first move, money just flies out of your pocket.
I would personally rethink selling your truck - if it is nice and newer and you love it. You will not be able to find a comparable vehicle - in all likelihood- for what you sell yours for in Texas. Many , not all , vehicles here are well used with high mileage. Just a thought from our experience

Depending on your job experience and type, give yourself plenty of time to find a *good* job. Generally on the mainland anyone could pickup a job to "get them by" until something better comes along. But here your entire cost of living is higher than Texas for example. So a "get you by" job on the mainland is a barely breaking even or in the hole job here.
Don't let anyones info. discourage you. Just really do your homework and try to have 3 months of total expenses saved for your move. You dont want to be in the position of having to move back to Texas in a few months.
Good Luck !!!!
Greg