Welcome to FT FlyMeToBelize!
Well, firstly, thanks for giving us all the information. So many people start out with a request like yours but fail to give the details. You have informed us of things that can help us help you.
I would also suggest NWA, but if possible--and I know it may be not your first choice--have some mileage in 3 airlines. Why do I say this?
There are basically 3 major alliances/airline partnerships. NWA is in the Sky Team, UA (while I agree what's been said above) is in Star Alliance, and AA is One World.
(Mark, I should just tell the OP to use AA hands down 

)
You say you
do wish to get status quickly on at least one, but if you have options with the others and start building in one per alliance from now, you will have more choices available to you in a pinch. ie, should you need to fly to X and do NOT have FF miles in an account, it would have been great had you saved some up while you were doing the bulk of your business travel.
That being said, what people have told you above is great advice. I would only add that you learn a lot about MILEAGE RUNS (there's a whole section of the forum dedicated to that) and CREDIT CARDS. I would--if you havent already--obtain and use a couple mileage earning cards and one I lilke the most is the STARWOOD AMERICAN EXPRESS.
There's also whole threads in FT about SPG (Starwood hotels) and the reason why it's popular is that you can use them to redeem for excellent hotels that happen to have very flexible redemption policies as compaired to other chains, but also because you can often convert points earned on your SPG account into airline miles!
Whichever airline you choose, get the credit card that helps you earn miles on it. UA has a Chase Visa, AA has the Citi Mastercard and NWA has a US Bank WorldPerks Visa. To get the best SIGN ON PROMO, dont just go by what you see in a seatback flyer or the company web site, rather, visit THIS thread and it will also help you with lots of cool travel and flight tips!
http://www.freefrequentflyermiles.com/index.htm
The author, PGary, is a regular poster in FT and other forums.
I would also participate in airline and mileage promotions. You can often find those in related links in airline-specific threads in FT. Do some browsing. You can also find those on PGary's site as well as on the airline sites you join.
Back to why 3 airlines;
I like AA because they have excellent redemption rules for award flights. One such perk is that you can start trying to book a flight with a phone agent and if you are short miles or they dont currently have a segment available for award travel, they can HOLD your itinerary for up to 2 weeks at times! You can just keep calling back in and if something comes available and your miles show up too, voila! They will continue to book for you and you'll often get what you wanted even if it's busy season!
I like NWA because of much of what was said above. I usually find they have newer planes and for me, I have found redemption for overseas travel to be pretty good over all. With NWA if you dont see an award flight on their website, call them and sometimes you will find they still do have some seats available! You'd have to pay the telephone booking fee but it's worth it at times.
WIth UA, I find if you are going to choose between them and US Air, you have better options for mileage use with UA.
My information goes around the horn here, but hey, as we can all eventually agree, there IS more than one way to skin a cat. Good luck and keep pressing!

MM