Joining a program -- or, more importantly, focusing on one airline -- might not be a "no brainer." You may just be better off choosing your for each trip on price and convenience. EgyptAir, Emirates, and Qatar can all credit redeemable miles (though not elite qualifying miles in the latter two cases) to UA. That, combined with your initial trans-Atlantic trip over, might result in a good portion of your flights being creditable there. (There are also a few regional fifth-freedom flights on UA partners, such as MCT-DXB on LX and DXB-CAI on SQ.)

I say this partially because the benefits of these programs are not great. For the Gulf carriers, you will accrue miles that may eventually get you a free trip, but they will not upgrade you (with rare exceptions) by virtue of status -- only U.S. airlines provide access to the front cabins without paying for it. I have been Gold (top level) on Qatar for a year now, and find the benefits marginal: the best parts are access to first-class check-in at a lot of chaotic third-world airports and access to lounges, although the lounges at the DOH home-base are poor. But there is no elite reservations/customer service phone number, elite boarding is rarely enforced, the redeemable mileage supplement you earn is low compared to U.S. airlines (e.g., a 50% bonus for top level on QR, EK, EY, and GF), and the airlines are not part of alliances such that you earn benefits on partners (except for MS in Star Alliance and RJ in oneworld).

If you choose on price or schedule for each trip, you can experience a variety of airlines -- Emirates, Qatar, and Etihad are excellent, and Royal Jordanian and Gulf Air (and seemingly Oman Air; I have not taken them) are solid -- with the flexibility to choose the best option for any individual segment. Keep in mind also that flying in the region can be expensive, and price often varies widely by carrier, especially by taking one carrier to a competing carrier's hub. (For example, if you want to fly CAI-DOH, Gulf Air through BAH will sometimes be cheaper than Qatar non-stop. And vice-versa for CAI-BAH.) So loyalty to one airline, as I have found with QR, can be a bit costly.

Also, you don't say whether you are moving to the Middle East long-term, or just taking an extended trip. If the latter, then of course will find that status and a bank of miles on a local carrier are not very useful to you when you are back in the U.S.