Which faction to pick?

First off, your class is irrelevant. There is no better faction for any one class. When you pick a faction, you must decide which two attributes/stats you want to focus on. If the story/role-playing aspect is important, that too will play a role in your decision (more information on their backgrounds is available below). There are three attributes:

Intellect: reduces the cooldown time of your super
Discipline: reduces the cooldown time of your grenade
Strength: reduces the cooldown time of your melee modifier

The Faction combinations are as follows:
Dead Orbit: DIS/STR
Future War Cult: INT/DIS
New Monarchy: INT/STR

An easier way to look at this:
Dead Orbit: Melee and Grenades
Future War Cult: Grenades and Super
New Monarchy: Super and Melee