This site is actually about backpacking as wilderness trekking, the standard American definition of "backpacking" and not budget travel. While most of us have traveled at one time or another, that is not our primary concern here.

There are some articles on the home page of this site, left-hand column about selecting and fitting backpacks. Note that the most important aspect of a backpack is fit, fit, fit! A poorly fitting pack means a painful journey. For your purposes, the pack must also hold up against the assaults of airline baggage handlers, who are NOT gentle. The lightweight backpacks most of us here use would probably not qualify.

As for a daypack, there are a number of those around whih are basically lightweight nylon sacks with shoulder straps, which work just fine for day trips while traveling but can be rolled up into a tiny wad in a corner of your backpack. Those will be less expensive, less bulky and lighter than trying to find a backpack with attached daypack.

I suggest you consult budget travel sites such as Lonely Planet, Rough Guide, Let's Go and Rick Steves. The last site has excellent articles on packing light and taking only carry-on luggage.