I have most of the popular ones:
Chase Sapphire
Amex Starwoods
Barclay Arrival
Capital One Venture
etc...
For flights the points/miles seem to be better than cashback.. Some of the flights can cost baseline $300 one way and I have found that you can get flights for 17000 points ( which is $170 ) when using miles/points. On cash back I'd have to have $300 one way.
Also, is travel your main thing? Reason I ask is cashback you can be tempted to spend on other things not travel. With this thought in mind, I like getting miles/points because even though I can transfer them around, Im almost forced to use them on travel.. which is what I'd rather do. It keeps me on my goals ( which is to travel ).
Make sure you get a card that allows you to transfer around, like Amex and Sapphire. You don't want to be stuck on a card that only allows you miles on Delta OR just gives you a "credit" back like Barclays. I'd much rather use my points upfront and get the discount ( $300 ticket vs a $170 for same flight ) and not worry about anything, then pay full price with cash/credit and get a credit back ( which means I am still paying full price and using more of my credit reward ).
I pretty much put everything on Amex first if I can and the rest on Sapphire. I'll use the barclay's credit on things like credit back reimbursement on car rentals or something.