As for flexibility, the SPG Amex (sorry it's an Amex) apparently has a deal where you get favorable rates on coverting those Starwood hotel points into airline miles, so that would be a way to go so you can hedge between hotel and airline programs (and have flexibility to go to any airline, not just the branded partner). The other big "double dip" card off the top of my head is the HHonors Amex which offers points on internet, cable, etc. in addition to groceries, drug stores, and restaurants. Sorry those are both Amexs, but those are two of the juicier cards out there.

I would say offhand that since you're primarly price-conscious, it might not be the best idea to get in bed with one carrier (say a branded miles card), so what might be the best alternative is to check out the Travelocity, Orbitz, etc. cards that would allow you to earn for your travel regardless of who you go with (assuming that site you tie up with offers the best rates of course). This could end up with the same issue as the airlines, where getting a Travelocity card might tie you down to them (even though you get to choose airlines/hotel chains) the same that getting a United card would tie you to United for earning purposes, so you wouldn't be as flexible going to Orbitz or Expedia. I'm not familiar with these cards so I can't comment on how good the rewards from Travelocity or Orbitz on their programs are.

My personal advice would just be to avoid any cards with fees on them, because your price sensitivity means that you don't care about the potential benefits of the fee associated with many airline cards, for example. Why pay $100 for an AAdvantage card when your travel might be on AA, DL, UA, FL in the space of a couple months?