Welcome to Star Wars the Old Republic! Whether you're new to MMOs or this is your fist, there is a lot of information that you need take in. My goal is to clarify some stuff that the game doesn't really explain, and point you toward good sources of information.
Unlike a lot of RPGs the drops in this game are not good gear at any level beyond about 15. You'll hear people refer to "blues and greens" ; this is referring to gear that can't be modified. This gear is generally considered junk because even if all the pieces in modifiable aren't at level, they have better stats than most things within several levels.
Orange Gear and Adaptive Armor
Modifiable gear is referred to as orange gear, because that is the color of the rarity of the gear. Artifact level gear, purple color, is also fully modifiable, but most of the gear people are wearing is orange. Orange gear's main stat, like weapon damage and armor rating, scale with the top modifiable piece. These include barrels, hilts, and armorings.
Each advanced class uses different armor ratings. Adaptive armor is armor that changes to the highest armor type your character can wear. The armor you'll need for your class is as follows :
Heavy armor : Bounty Hunters/Troopers and Juggernauts/Guardians
Medium armor : Agents and Marauders/Sentinels
Light armor : Inquisitors/Consulars
Planetary Commendations are going to be your primary currency for getting the mods, enhancements, hilts, armorings, and barrels you need to gear yourself while leveling. If you see a planetary comm as a reward for a quest you should always take it unless there is orange gear with modifications you need or modifications you need as rewards. Planetary comms can be traded in at vendors on the fleet in the supply section.
Besides planetary missions, you also get planetary comms from doing flashpoints through the group finder, completing specific flashpoints for daily quests you can pick up from the priority mission terminal on fleet (also in the supply section), and converting the warzone comms from pvp into planetary comms.
There's a really good guide for stats and why you should focus on your class's specific primary stat here.
It's really long, but a good read. However the short version is:
Your class's primary stat raises more than just your damage, where as other class's primary stats either don't help at all or only raise damage. Copied from that guide each class uses:EMPIRE
Bounty Hunter (Mercenary/Powertech): Aim
Imperial Agent (Operative/Sniper): Cunning
Sith Inquisitor (Assassin/Sorcerer): Willpower
Sith Warrior (Juggernaut/Marauder): StrengthREPUBLIC
Jedi Consular (Sage/Shadow): Willpower
Jedi Knight (Guardian/Sentinel): Strength
Smuggler (Gunslinger/Scoundrel): Cunning
Trooper (Commando/Vanguard): Aim
Secondary stats include critical rating, surge rating, power, accuracy, alacrity, shield rating, absorb rating, and defense rating. A lot these become much more important once you get into the endgame at level 50+, but you will run into some of them while leveling especially as you approach level 50. There's an explanation of each at the end the post I linked to above. The big thing to know is power is always good for dps and healing, while tanks need to just grab whatever defensive stats they're able to get while leveling. If you're a tank Sixdark has linked to a really good guide to tank stats endgame here.
Knowing Your Class:
One of the biggest things is just knowing your class. What it can do, what it's good at, what secondary stats are good for it etc. The site you're going to want to use for this is Dulfy
It has guides for each advanced class for both the republic and empire; use the dropdown at the top to find your class. While the guides are made for endgame, studying them as you level will help immensely in making yourself better.