Depending on how familiar you are with the various battleforce special abilities you should be fine with just the 9 pages for Quick Strike, the starter rules for BF, the to hit modifiers page for Quick Strike, and the index page which has the critical hit charts for BF. Once you get most of the rules into your memory then you'll really only need the to hit modifiers and critical hit charts.
If you're not overly familiar with the various special abilities for Battleforce such as Heat, the various weapon codes such as Indirect Fire, LRM, and Stealth then you might want to print out those pages as well.
Also read up on them, and some of the rules governing heat, transports, and the ways that non mech units differ from battlemechs.
Though to be honest I just went and picked up a hard copy so I'd have all the pages handy when I am playing. Not only does it let me quickly reference things that I'm not familiar with, but I can also show people the exact wording of the rules so that they also fully understand them.