I just got the Osprey Radial 26 for my birthday. It's a backpack specifically designed for bike commuters and has a suspension system to keep the pack off your back so you get airflow back there and don't get (too) sweaty. Plenty of room for a sack lunch and clothes. Also has a "lid lock" so you can easily attach/detach your helmet to the outside of the pack. They also make a 34 L size if you want a bigger one.
http://www.ospreypacks.com/us/en/product/radial-26-RADIAL26.html
Shop around...don't pay $170 obviously.
I used my $30 hydration pack from Costco yesterday. It also has the suspension system to keep the pack off your back. I only had a bit of water in there - decided to keep most of the weight for my clothes/shoes/lunch. It was OK - I much prefer strapping stuff onto my rear rack because
- even with the suspension system, it is a little sweaty. I kinda like a bit more freedom when riding
- I'm stuck to wearing sporty clothes and I often wear my work clothes when biking to work.
- in continuation of above, I know I'm not being super practical - but from a fashion perspective I just don't care for biking to work in sporty clothes and a backpack. I kinda like the feel of biking in work clothes, especially when I wear a dress. I just change my shoes when I arrive and I'm set. Plus it means no one sees me until I'm work-ready (I change my shoes and add jewelry when I store my bike). If I need to change, I have to come into the office and while its fine, I prefer to avoid it.
In conclusion, strapping a small bag onto my rear rack with bungee cords has been cheap, practical, easy, and suits me. I still drool over pretty baskets and panniers (especially the $60 set from REI posted above!) but I think this will serve me just fine for now. I add a milk crate when I go grocery shopping. Not so crazy about the milk crate but I figure at least I am not going to work with it. (and yes, I'm finding I'm a little vain - I absolutely don't want to ride to work with the milk crate).