Paul,
I'm pretty new myself, but I can speak somewhat intelligently on a few of your questions.
First, very smart on you for using your (I assume) Post 911 GI bill. It's the best deal in town I think you are pursuing a terrific major. I'm a few weeks from finishing my Masters and all six-ish years have been on Uncle Sam's dime.
ok..
1. Like previous posters have said, the VA doesn't actually make the loans, they guarantee them and the big kicker is the 20% down payment is waived (and PMI!!). I have not used the VA loan yet, but I intend to on my next property and roll the equity in my current house into a couple rentals. It's a powerful thing freeing up equity to use for investments. HELOCs are tough to get so the VA could be a good route to get a place to live, build SOME equity, and free up your cash for investment properties. If you plan to move around, though, I'd probably just rent.
2. I have to disagree with Andy in regards to USAA. I've been personally using their services for banking, mortgages, insurance, etc. and I have been nothing but thrilled with their customer service.
3. I wouldn't worry about owning in cities other than where you live, as long as the deal is good and can cash flow INCLUDING property management costs. I actually think it is a good strategy to own properties in places you like to visit or where family lives. Part of your trip can then be tax deductible (consult your tax person)
3. Hotels are probably a good long term goal. They tend to have low failure rates, at least the franchises do (check entrepreneur.com) Problem is you are playing with the big boys and NO franchise "gives you money" quite the opposite. You give them A LOT of money, and their net worth requirements tend to be prohibitive to the small guy (read MILLIONS).
Done rambling. Good luck!