Each faction provides its members a mechanical advantage in the form a choice of two 5 point bonuses.
For attribute bonuses, keep in mind that once all points are spent, ranks below Amber must align to either Human or Chaos levels. So, even with a 5 point bonus to Endurance, a character must still spent another 10 points to take that bonus and get to Chaos level.
Black Blood offers either 5 points to Warfare (to represent advanced combat training) or 5 points of Allies throughout the military industrial complex.
The Order offers either 5 points to Psyche (to represent psychic defence training) or 5 points towards sorcery, as one of the few groups with access to ancient grimoires.
The Grail Society offers either 5 points to Psyche (as a result of spiritual meditation) or 5 points in artefacts, from raiding the Vatican's hidden archives.
Tarot Corporation offers either 5 points to Strength, or 5 points towards Shape Shifting. Tarot pushes it's employees physically and is not above secret experimentation.
The Double Helix Club offers 5 points to custom, non-ADRPG powers, or a personal Trump deck and 3 points of Allies.
The Independants offer 5 points to Endurance (surviving alone isn't easy) or 5 points to Stuff (if you're not tough, you'd better be lucky).
Example 1: Susan is building a warrior nun of the Grail Society name Sister Immaculata. As her bonus, she picks artefacts, and gets a 5 point holy sword (deadly damage, plus alternate form: crucifix).
Example 2: Burt is building a Tarot operative named Elton. Elton's main focus is his custom power (telekinesis, which costs him 20 points), so he goes with the Strength bonus. Most of his points are in Psyche and Telekinesis, but he spends 10 points to bring his Strength up to Chaos level.