Back rack good for commute?
Counter to the answer that 'cmaster - reinstate monica' gave, you CAN put your backpack directly in a basket on a rack. It's easy!

Install a rear rack as many other answers suggest. If you're not comfortable doing this yourself, have a shop do it for you. Get a full rack, not one that relies on just clamping to the seatpost.
Get a milk crate as a basket. Don't laugh! Milk crates are often easy to find and can be free if you look around hard enough. They're tough and are not affected by water or temperature extremes. They have wonderful handles that assist in moving your bike around.
Attach the milk crate to the rack using metal hose clamps. You might be tempted to use zip-ties. Zip-ties do work (for a while), but become brittle with age and will break at the worst possible time (when your crate is heavily loaded).

Putting your back-pack in your milk create is easy! Just throw it in! The high walls will make sure your bag stays in. If you're concerned about it falling out, use an old innertube tied between the handles on the side. (An old innertube makes a great tie-down for other things in your crate as well!)
Your bike is now much more useful. You can stop for a bag of groceries which fit nicely in the rack (and your back-pack can go on your back for that leg home from the store).
Do a google image search for &quot;milk create bike&quot; and you'll see some examples.