I'm not a big fan of Hilton ... as their program seems to be in a lower class compared to Hyatt or SPG. However, if its suiting your needs, I wouldn't necessarily look to change right away.

I'd recommend the following-

1) Research both Hyatt & SPG, which are both more of 'luxury' brands. Better for resorts destinations, etc. If they have hotels in your preferred destinations, might want to consider switching down the road.

2) However, if you determine that Hilton is the right way to go, and its where you are staying on most of your visits, HHonors offers cards from both Visa & Amex. I believe they are similar, but you should look into each. Remember that Visa is more widely accepted than Amex, so if you plan to only have 1 card, that might be the better route.

3) I dont know what car rental company you're using, but that amount of rental usage should definitely warrant (a) signing up with 1 company and sticking to them and getting car upgrades, free rental days, etc. and (b) seeing what rental companies Hilton partners with so you might end up with some better deals, transfer points, etc.

4) American offers the Citi Mastercard and/or Amex with 25k sign up bonuses, with certain conditions. AA's program is generally regarded highly for award earning/redemption and ability to transfer to partner (both One World and codeshare) airlines.

Realistically, my general opinion is something along the lines of:

HHonors Visa Card from Citi
AAdvantage card from AMEX

or

HHonors card from Amex
AAdvantage card from Citi (Mastercard)

Depending on whether you are flying AA more or staying at Hilton's more, and how you are going to be using your cards (remembering that AMEX is not as widely accepted).