Do not buy a car battery. Been there, done that.
Car batteries are not sealed, and they give of poisonous gasses as they are used. Furthermore, they are meant for cranking a few hundred amps for a short period of time. They are not meant to be deep-cycled. That is, if you discharge them and recharge them, they will only last about 3 or 4 charges before they are useless to you.
I used to carry around a car jump starter battery. These are the kind that contain a sealed lead-acid battery. They usually have accessory jacks on them, which you can plug in a small 100W inverter and run your laptop on all day. My last battery would run my laptop and 4 routers (don't ask) for 14+ hours. These are perfectly safe. However, the one I had didn't have removable alligator clips, and I was always worried they would come in contact with each other in my backpack and weld themselves together and blow up the batttery.
I have since switched to one of those xPal/Energizer batteries that run your laptop/camcorder/cellphone for a few hours. However, my laptop is power hungry and their biggest battery only runs my laptop for 45 minutes.
In short, go with the car jump starter if you can. Best to find one with detachable, or at least coverable, clips.