There's no reason not to do both, once you get your feet wet, and you might as well throw in UA at some point. There is decent availability on the LH DFW-FRA flight that you can use to get to virtually anywhere since you can route through Europe to Asia or Africa. And AS (I'll stop here and try to limit the info overload).

All 4 programs offer one-way redemptions and the one thing you will likely find if you do some searches is that it is often better to use one airline/alliance for one way and another for the other.

I would not apply for an AMEX Gold with less than 50K points. Watch your email, mailbox, cardmatch.com and these forums. For N. American nonstop flights on AA, BA will usually require less points, have no close-in booking fees and have more favorable cancellation policies. You can transfer both AMEX MR and Chase UR to BA.