If the extra cost isn't a bother, biz class is definitely worth it for the comfort. You should be able to arrange your long-haul segments to include flat beds, and I can't say enough about what a difference that makes to arriving in pretty good physical shape. I'm convinced that some large part of what coach travelers think is 'jet lag' is body stress due to the confined/uncomfortable seating.

"Extra miles" are usually secondary unless you have a specific mileage goal.

At the moment, aadvantage allows you to qualify for status using either "q-points" or miles, and premium-class trips earn 50% more points than miles. But aadvantage offers (at present, USdbaAA isn't finished birthing, so anything may change) a "platinum challenge" which earns platinum status for signing up, paying a fee, and earning 10,000 points in a short period. So this time around you don't have to be a mileage whore like the rest of us, scrabbling for our 50K miles or points.

If you start (and end) your trip at (selected places) outside the U.S. you'll save a lot of money. Starting a 3-continent biz-class trip (DONE3) from Cairo will cost you $6020 (plus significant taxes); from any U.S. city it'll cost you $10199 (plus about the same taxes).

You can fly in biz NYC-CAI for around $800. Getting home after the trip should cost less, or you could use some of your newly-earned miles.

I knew Egypt was cheap but didn't look for cheaper places.

Starting overseas also means you can split your trip into two parts. You have a year after you begin to be done with it, so might spend some time in Europe, come home to the U.S. and use your North American segments at your leisure (N.A. includes Central America, the Caribbean, up to Alaska, but not really Hawaii) and then when you're tired of that, continue westward around the world. It works the same flying east, of course.

Starting overseas slightly complicates ticketing. That cheap fare is intended to benefit poor Egyptians, not rich Americans, so there are kinda-rules about ticketing.