My daughter (first child) was born in late February and I've been using the messenger style Fila diaper bag. It's worked well so far.
I wasn't sure if I wanted the backpack style, or the messenger style, but think I made the right choice. The messenger bag, when worn across my chest, keeps my hands free, but is still accessible on my hip without having to remove it (like you'd have to do with a backpack.)
The material is pretty thin, but for the price it's been a really good buy. I was recently at a baby store and they had messenger-style bags geared toward dads that were more than $100. Granted, the quality was probably higher, but for almost 10x the price, the Fila bag works fine for me.