Embrace the Shadows will be a guide of sorts through creating, levelling, and playing a Shadow Priest. I'll be making the assumption that you are not making your new character on a server with higher levelled mains, so I won't go into twinking or AHing expensive gear. (Talk to Og for that. =P ).
The first choice you'll be facing on your quest to become one of the darkened few will be that of race. Now, obviously, I'm going to tell you to choose Troll. Best dance, best jokes, best language, etc. We're amazing, I know. =P
To be honest, of all classes, choice of race matters most for Priests. This is because in addition to racial abilities shared by all members of a given race, priests have class racials. Now, between that and the hybrid nature of the priest class, each race needs a bit of an introduction.
Human - Humans have pretty lackluster class racials. Feedback is a short-duration personal buff that burns mana from attackers who hit the priest with spells and Desperate Prayer is a self-only instant cast heal on a ten minute cooldown. The Human racials however, are pretty good for PvE healing priests, specifically The Human Spirit which passively increases Spirit by 5%. Diplomacy is also nice, increasing reputation gain by 10% which makes the hardcore TBC rep grinds slightly less daunting. For Shadow Priests, Humans are a subpar choice for race. Desperate Prayer is a Holy Spell and therefore not castable in Shadowform, and Feedback is generally bad for all types of priests, although the shadow damage component is somewhat nice for it's ability to proc Shadow Weaving and Blackout on the spellcaster who hit you. If you have to be Alliance, I'd suggest a different race.
Dwarf - Prior to TBC, Dwarves were the race for a PvE healing priest. While they share Desperate Prayer with the Humans, Fear Ward was what made Dwarves so sought after. However, in patch 2.3, Fear Ward was changed to a trainable priest spell and in it's place Dwarves were given Chastise, a Holy Spell that incapacitates the target for 2 seconds. Dwarven Stoneform, shared by all Dwarves, is a strong spell for PvP. It removes all poisons, diseases, and bleeds and makes the dwarf immune to them for 8 seconds. For a PvP Shadow Priest, Dwarves would be a solid choice, but for PvE, there are better.
Draenei - Draenei are one of my recommended races for a PvE Shadowpriest. This is because of two things. First, they have a 1% hit aura with spells which lowers the need for hit rating even further. More importantly though is one of their class racials, Symbol of Hope, which returns about 1000 mana to everyone in your party over 15 seconds. With those two racials, Draenei are a solid choice for casual raiding. Not having to aim for gear with lots of hit rating on it and being able to supplement a low +dmg Vampiric Touch with SoH make draenei very strong at early raid gear levels. In addition to SoH and the hit aura, Draenei get Gift of the Naaru, a free renew on a 3 minute cooldown, and Chastise, which they share with the dwarves.
Night Elf - I never thought I'd say this, but I'm recommending that new PvE Shadow Priests who plan on raiding end game content choose Night Elves. At the Tier 6 level (and even late Tier 5), a Night Elf shadow priest will always out damage any of the other alliance races because of their once worthless class racial, Starshards. Starshards previous to patch 2.3 was a joke. A channeled Arcane spell that did barely any damage, its only use was to draw an Interrupt to allow a PvP priest to cast Shadow/Holy spells safely. After the patch however, Starshards has been changed to an instant cast DoT with a 15 second duration and a 30 second cooldown. This free damage alone is worth more from a pure PvE standpoint than any of the other race's spells. Not to mention Shadowmeld, the Night Elf racial which allows for stationary stealth, which is amazing for people who find themselves going AFK frequently in dangerous areas. All these points actually completely overshadow the new and improved Elune's Grace, which lowers chance to be hit by melee and ranged attacks by 20% (Previously, this was an increased chance to dodge, which let Warriors go to town on Night Elf priests).
Horde (FOR THE HORDE!)
Undead - With Will of the Forsaken, the undead racial which removes fear, charm, and sleep effects, in addition to Devouring Plague, a high-cost DoT that returns health equal to damage dealt, the Forsaken are a strong choice for PvP Shadow Priests. Their other class racial is Touch of Weakness, which is also more PvP-focused. It is a self-buff that causes the first person to attack the priest to take a small amount of shadow damage and be afflicted by a debuff reducing damage caused by 35 for 2 minutes. The damage reduction isn't that great, but the shadow damage component, like Feedback, can proc Shadow Weaving and Blackout.
Blood Elf - Like Draenei for the Alliance, I believe Blood Elf is an moderately good choice for a Kara-level raider. Mana Tap/Arcane Torrent (Blood Elf racials) allow for a small burst of free mana every few minutes. For class racials, Blood Elves got kind of gypped. Consume Magic is another possible method for Blood Elves to get some free mana, but it removes a random buff on the priest in exchange for a small amount of mana. Now, if you get lucky and consume a renew with only 1 tick left, then great, but just as likely is consuming your Prayer of Fortitude and losing an expensive buff and gaining not even as much mana as it costs to cast. They also share Touch of Weakness with the Undead. Overall, Blood Elves are a mediocre choice for either PvP or PvE.
Troll - Easily the best race in the game, there is no reason to ever not be a troll. Seriously though, I personally recommend Trolls as the best race for pure PvE Shadow Priests. The key here is the Troll racial, Beserking. Beserking increases haste by up to 30% based on health at the time of casting. A timely Shadow Word: Death can drop your health just long enough to pop Beserking and your trinket for a nice bit of burst on a boss fight. Troll's priest racials aren't amazing for PvE, but are pretty nice defensively for PvP. Shadowgaurd is a shaman's lightning shield, only with shadow damage and therefore chance to proc Shadow Weaving and Blackout (I'd also like to note that on some PvE fights, Shadowgaurd can give you free dps on the boss because AoE spells will proc Shadowgaurd on the boss). Their other priest racial is Hex of Weakness, which is the same debuff as applied by Touch of Weakness, but targettable and which also reduces effectiveness of heals on the target by 20%.
Phew, that was longer than I expected! To wrap it all up, I'll just restate my recommendations for PvP and PvE per faction. In my opinion, Alliance PvPers should choose Dwarf while PvEers should choose Night Elf and Horde PvPers should choose Undead with PvEers choosing Troll. However, I'll be the first to tell you to never choose a race that you'll hate specifically because of powerful racial abilities. You'll never have fun with your priest if you rolled a Night Elf even though you hate the race with a passion just because of a few dps increase in 70 levels and 3 tiers of dungeons.