Well, this August I flew to NC to see my new granddaughter, and I took one regulation size carry on rolling suitcase, and one Schlep Bag (free online pattern) that I put a small purse, my laptop, a book, and several snack things into. I can cram lots of stuff in it, and it's pretty light unless I try to carry too much heavy stuff. It's pretty large for a tote, so I kinda do tend to carry too much. But it works out great, and I can twist the handle around the handle of the rolling suitcase and wheel them both through the airport. That's what works for me.
All the liquids have to be 3 oz or less, and all have to fit into 1 (one) zip lock baggie. I don't take any with me...just buy small ones at WalMart when I get to destination. You can carry any bag that you can cram under the seat in front of you. They only make you check your carryon if you are flying on a small regional plane and the carryone won't fit in the overhead....and they don't charge for that. I never check bags onto large planes any more...they all charge for it now.