My old commute would change your mind;I used to climb Nebraska/Loughboro from Sibley to Ward Circle every day.

I think you should get something decent since there's a good chance you'll be keeping the bike for trailer/childseat duty. If you'd be willing to entertain the idea of a hybrid,you'll find a lot more to choose from.

If you go used,avoid anything with steel wheels. They suck for braking in the rain,and are heavier than they need to be. Biggest thing with used bikes around here are making sure the wheels are true(crappy roads take their toll and many owners don't seem to notice) since if you can't true them yourself most shops are going to charge $30 or so a pop. Also,used bikes tend to hold their value since there's such high demand in this area due to the transitory nature.

As for trailer vs childseat;I've got friends that use both. Biggest thing about the trailer is that it basically extends your bike way back,but they're also lower to the ground so you def want to have a flag and they will push the bike on downhills and under braking. Seats are cheaper and some come with integrated racks. I've had lots of folks come to my clinic with Topeak systems;the seat pops right on/off the rack and when off you have a standard rack for panniers/etc.

One other thing to consider is a cargo bike. Xtracycle just came out with a new 'compact' cargo bike that has all kinds of kid-friendly accessories.