I think you could try the Presidential Plus card from Chase for a bit of help on United. I'm not sure of specifics, but the fee is hefty. Likewise, the Marriott card has some status accumulation points. The surpass HH Amex also gives top tier for 40k spending, so you may want to look into that if you aren't completely set on Marriott.

Lastly, I agree that some combo of cash back cards would also be good. You have to breakdown where you'll be spending to really figure out the specific card. You should be shooting for 2% or better.

Again, I'd probably wait until after your mortgage clears before putting in a bunch of credit card apps...but after that is done is when the fun begins.