I have a relatively well geared Sniper myself (BH with a few WH pieces) and here are some (hopefully useful tips) on how to play it. Your experience gets better which each step you implement.
1. Pick your spec carefully. Personally I play Marksmanship becuase Engineering just doesn't feel sniper-y enough for me. Marksmanship is an awesome single-target killer spec (which I think snipers are) but Engineering is more useful for defending objectives. You probably get a bit more damage out of Engineering because of all the AoE effects but fewer actual kills for the same reason. I recommend avoiding Lethality because of the Lingering Toxins talent. Putting a 30-sec long debuff on players makes them immune to cc and mezz and that can be a problem in many situations.
2. Positioning is alawys critical. The Sniper AC is very terrain dependant. Always pick an inconspicious location well behind friendly lines preferably with some hard cover, too, nearby. As you're an unencumbered heavy hitter, tanks will be thrilled to taunt you and reduce your overall dmg by 30% (at least I get taunted quite often if I give them the chance). Watch out for tanks and stay well outside of taunt range!
3. Avoid 1v1 situations if you can. Especially against melee. While it's not a bad class 1v1, it's not a great one either unless you have a terrain advantage (like a ledge or something). A marauder, a jugg or a tankasin can tear you a new ***hole pretty quickly if you let them get close. I tend to run away quickly into large friendly groups if I see a melee single me out. (Remember that while you're unjumpable, Sins can use Force Speed and Maras Predation to quicky close in on you.)
4. Change positions frequently. Staying in one place for too long will get noticed. Also there are other benefits associated with moving periodically like an instant Snipe (Snap Shot) and passive damage mitigation (Ballistic Dampeners).
5. In Marksmanship your attacks can do tremendous single-target damage but they are also vulnerable to line-of-sight issues. Try to pick targets in big open areas with few pieces of cover available. If you are focusing one target down (like a healer) look around where he can run to for cover if his HP gets too low before you engage him.
6. Watch for counter-snipers and gunslingers. If you see one, open with Diversion. They (you) are nothing without cover. If they (you) can't take cover and use essential skills, the Sniper dies very quickly. If you get hit by Diversion stay behind hard cover until the effect is gone.
7. While you're a single target killer, don't neglect AoE skills! Snipers get two awesome AoE skills even in Marksmansip spec. Place Orbital Strike periodically on objectives you're guarding like doors, nodes etc to prevent a stealth cap. Suppresive Fire is often overlooked (as it does quite low damage) but it's a great anti-stealth instant AoE skill like Stealth Scan or Hail of Bolts. Most Maras, Sins and Operatives (and their Rep counterparts) tend to vanish around/below 30%. Have Suppressive Fire ready to counter their last ditch attempt to escape. (I know good players use Force Shroud and Undying Rage in this case but visible usually means killable.)
8. Use Leg Shot before Ambush. Ambush puts a very noticable red marker on the target for all to see. It's their clue to run away if they want to live. Good players can often find cover in time. Deny them the opportunity by immobilizing them before you target them with your biggest attack.
9. Use your mezz to interrupt. Interrupts are a weakness of the Sniper because one 12cd rupt is oft times inadequate against a healer for example that can throw out large heals every 4 or 5 seconds. I usually use my normal interrupt on Salvation/Revivification and Flash Bang when they try to get their HP back up with Deliverance/Dark Infusion. This leaves the enemy healer vulnerable for a quick Snipe, Takedown and Followthrough (which at low HP usually kills them) before they can get off another big heal. Multiple people focusing the same healer helps, of course, while another healer healing your target hinders you.
10. As much as it pains me to say, go Biochem or Cybertech. I would recommend Biochem because of the short range on grenades means you'll be using them less often than melee classes. Still, I always like to have a few Seismic Grenades ready just for that pesky Mara that wants to wave his glowstick in my face. (Also, unless they're really low on HP, I'll just stun and run away.)
Been called a coward for running away from melee but it's what I do. I know the strengths of my class but I also know the limitations.
Hopefully this short (?) guide can help you to become a real killer on the battlefield and will enjoy reading it just as much as I enjoyed writing it.
This, should be stickied!
I'd like to add one more point;
-You are considered as an easy kill, use this as an advantage to draw attention when capturing a node or so. The morons will chase you while the node gets captured. Works every time.