When it comes to air travel, hands down the best "bag for your buck" is a plain old back pack! It fits a fair amount of stuff, it's hands free, it fits under your seat (so no worries about finding overhead space) and it counts as a personal item, not a carry on so can still bring a larger carry-on if needed. And you can use it during your trip as well if you need to go out-and-about and have a lot of things to carry along.
I used one when traveling with my DH and DD in April. I had the backpack and with both hands free I could easily handle DD in the stroller (which we gate checked) and DH just had his mini-cooler with his meds and the car seat strapped to a small wheeled cart (which also worked perfectly, he wheeled the cart up the airplane aisle, installed the seat, collapsed the cart and stuck it in the overhead in no time flat!).
I have NEVER moved through an airport so easily!
My other travel fav is having a small thin wallet that I can easily tuck into my front pocket. It has my credit card, room card, license, health insurance cards, and cash. I put my cell in one pocket and the wallet in the other, and the purse stays in the room. Makes for easy park touring, city sightseeing, etc. No worries about forgetting my purse, purse snatchers, or just the general pain of having to carry something around all day. If I just have to carry something else, the backpack I used for the airport does double-duty. But because the wallet is in my pocket and not the backpack, if the backpack gets lost/stolen I'm only inconvenienced and not totally screwed.