1. How should I go about playing the game to get the best experience possible?
The game was really designed to be a story driven MMO, so doing the PVE storylines is how it was designed. Companion unlocks, ships, and legacy unlocks are all tied to your class storyline progress.
However, there are plenty of other options for leveling (PVP, space combat, etc.) if that's not for you or you need a change of pace.
2. How do you get all that awesome unique gear I see people with. While I'm playing I only ever manage to get a hold of generic boring armor and weapons, yet I see all the people while watching videos or playing the game with awesome stuff?
You get it as you level, but it can be hard to get a full matching set w/o focusing on it or knowing where to look. The later game armors tend to be fancier and some of the low end stuff is just ugly (BH helmets for example).
If you open up the character screen, on the lower right of the "paper doll" is a button that will allow you to match colors which goes a long way to making you look better.