One variable is the fair bucket you buy. If you pick United as your FF choice, some fairs on Asiana and Turkish won't accrue any PQM (butt in seat) miles that count toward status. Some fairs will accrue PQM, but with only 50% or even zero award miles (traditional frequent flyer miles used redeemed for tickets/upgrades).

I would say either Asiana or United, with a lean towards United since you have some domestic travel in US plus the European hop. Turkish makes no sense unless you always plan to fly with them and they are not convienent for most European cities from North America. Unless you like to backtrack hundreds or a thousand miles with a connection and extra flight every time you go to Europe. Out of JFK, I would make good use of all of the *A carriers who have non-stops to places you go to. Asiana to Seoul, the half dozen carriers with non-stops to major European hubs like Lufthansa and Swiss. That kind of thing.

Going with Asiana would really depend on their upgrade policies, which I don't know and am too lazy to look up. If you're flying coach in Asiana though, I would go with United as the FF program. You won't loose anything.

With a couple of transcons, a couple of TPACs and a TATL each year, that's around 50,000 butt in seat miles each year. That will get you Gold status, both on United and Star Alliance. You can use the airline clubs on all of the carriers on your international trips, you get the extra baggage allowance, etc.