If you are really backpacking. YOU need a backpacking bag. Not Rick's bags.
Check into High Sierra brand internal frame bags. Here you get really good quality (selected by Outside Magazine as a BEST selection) and a great price/value.
If you need a good bag for really hiking/walking around, find one with internal stays and a frame sheet, a good waist belt and lumbar support.
For 3 weeks, you should pack for 1-1.5 weeks, leaving room for stuff you may buy on your journey.
I'd recommend you make sure you buy the bag to FIT your body. Just running out and buying a bag like this because someone says "this is the best bag" is wrong. You should make sure you have your torso length fitting the bag. This isn't rocket science, it's easy, just measure from bottom of neck to top of waist, then match to the correct size bag.
Check into the follow models: Summit 45, Explorer 55. No need to go larger than these too sizes. The great thing about these bags is they also come with a rain cover. Think about walking in the rain to find your hostel, or to get to the train station without this feature...not fun, and lots of wet clothing.
Here is a link to the bags on ebags.com
http://www.ebags.com/high_sierra/summit_45/product_detail/index.cfm?modelid=88520
http://www.ebags.com/high_sierra/explorer_55/product_detail/index.cfm?modelid=88521