People have different preferences for carry-on & checked bags, so there's no one "perfect" solution for you. Personally, for most of my trips (certainly international) I have a small rolling bag (makes those occasional long immigration lines or treks through terminals easier since I don't have to hold the weight of my bag) and a thin tote that goes under the seat in front of me and holds my in-flight essentials.
I have a 19" Eagle Creek (
http://www.amazon.com/Eagle-Creek-Ho...1097387&sr=8-2 )
Typically I'll use a LeSportsac nylon tote, but I also have a Briggs & Riley tote and a Timbuk2 tote I might use, depending on the trip. LeSportsac fits easiest under the seat since it's thin - the other bags are stiffer nylon and don't smush as easily.