First, Pair order DOES matter. Depending on the manufacturer, the insulating material can change from pair-to-pair, the twist-rate varies from pair-to-pair (orange is usually the most twisted), and the manufacturer designed the cable with a specific pair-order in mind, and chances are the cable meets Category specification only when the cable rigged in either 568a or 568b.
Second, when the cable is run throughout the building, terminated in panels and faceplates, it's generally referred to as "Structured Cabling." The concept of structured cabling grew out of the situation where every kind of computer or phone device needed different cable (coax, twinax, "Rs232 stuff," "phone wire"....). The Structured Cabling specification provides infrastructure quality sufficient to run computer networking, phones, terminals (with baluns/adapters), baseband video & audio (with baluns/adapters), RF/cable TV (limited but functional), RS232, and some other application-specific functions.
Third, terminate all four pairs; trying to snake four of the eight into the right slot of the RJ connector is a right royal pain the the a**. Line 'em up (all eight wires) and they slide right into place. If you want to split the function of the cable (not recommended, BTW), break it out at an outlet box, or create a "breakout cable," that plugs into the outlet then splits.
The correct pair-orders are:
568b (most popular these days): white/orange, orange, white/green, blue, white/blue, green, white brown, brown.
568a : white/green, green, white/orange, blue, white/blue, orange, white/brown, brown.
This order is left-to-right, with the clip-side down or away from you. If you got it right, it should look like white|color|white|color...all the way across. Note that the BLUE pair is reversed (blue, white/blue).
There should be no more than 1/2" of exposed/unjacketed wire, and the jacket should get crimped inside the connector. Part of the RJ connector is designed to crimp down on the jacket to provide strain relief.
If you can't do it right, get someone in that can. Improperly installed/created cable WILL mess up your performance. Most of the time it ends up showing as intermittent problems...usually when the cable is loaded...like long file transfers.
FWIW
Scott