Change the appearance later in the game

If the class armor is not from a faction (vanguards don't count here) then it's just for decoration. If it is a faction's armor bit then you'll earn rep for them instead of for vanguard or generic crucible faction.

In either case, rarity has no particular effect.

Note that even with faction armor equipped that turns vanguard rep into faction rep, you'll still get vanguard marks for missions that give them. Since faction vendors only take crucible marks, this may affect your strategy when gaining rep.

You can get Strange Coins, Motes of Light, and Ascendant materials from Earth public events, I don't believe public events ever give gear/weapons.

This indicates that public event rewards are not tied to the area. You might as well do them on Earth as they are easier due to the generally low-level mobs.