I have tried various backpacks and this one on the right, the Osprey Farpoint 70, is by far the best backpack I've ever found. Comfotable, with straps that actually bend and sit snuggly on the hips, enough space to carry a lot of stuff but not cumbersome, shoulder straps can be sealed away for flights, the day pack is a good size (and not too ugly) and the material is really lightweight. If you'd like to read more detail on why I think these features are so important see How to choose a backpack.
As long as the bag is not packed till it's bursting at the seams, or with lots of heavy books, it's a good size for keeping your luggage weight under 15kg (33 pounds), which is very useful as a lot of airlines charge extra if your bag weighs more than this. It also comes with a LIFETIME guarantee. Osprey will repair any damage to the bag, whatever the cause, no matter how long you've had it and if they can't fix the problem they will replace the bag instead. Osprey bags are expensive, but when you factor in that it may be the only backpack you ever need to buy, the price starts to look a lot more reasonable.
If I were to do it all again, I would buy a smaller bag so I only have handluggage. The Osprey Farpoint 40 is the bag I'd chose for this since again it's good quality and it has a remarkably large amount of space given it's a carry-on bag. You'll still want a daypack so you don't have to empty all your possessions from your main bag to go out during the day. To allow you to easily carry both bags, get a stuff bag, like the Osprey Ultralight Stuff Pack on the right, which folds down into it's own little pouch whilst not in use.
I forgot to take a rain cover for either my big backpack or my day bag when I left for this trip. An oversight I strongly regretted when having to walk through a thunderstorm for 20 minutes with all my possessions on me to find my hostel. Needless to say eveyrthing I owned was soaked, and it's very hard to find enough space to dry everything you own in a hostel dorm room. Don't make the same mistake I did. It's worth getting a rain cover for your big backpack such as the Osprey Ultralight Raincover on the right, and also for you day pack. I ended up buying the 25L version of the Karrimor Dry Bag shown on the far right, for a friend to bring out, since it is big enough to put my day bag in but can also be used as a drybag for day trips on boats etc. whereas a rain cover wouldn't have had this versatility. This drybag is made out of thin material, which is needed to be flexible enough to fit my day pack in, but that does mean it is not 100% waterproof. It is not a robust enough dryback to go for a swim with however it does suffice for keeping your possessions dry in the rain or when being splashed with water on boats.