If you have a place at work to stash shoes, a shower kit, towel, etc. that will work better in the end. By the same token I'd put the flat kit in a seat wedge or some other place on the bike itself in case you get a flat and aren't carrying the backpack.

You'll still a need a backpack, panniers or something but the less you have to carry IMHO, the better.

If you need something waterproof the Banjo Bros. Commuter Backpack is fairly inexpensive (for a waterproof backpack) and it comes in two sizes.