Well, first off, Welcome to WoW, JessicaStarr. I'm happy you're playing, or I'm sorry you have started your addiction, as the case my be.
Just a note about priests, after level 6ish, the going starts to be tough. It pickes up again around level 40ish. You will notice it get a bit easier every level, but all in all, 40 is where you will really notice the take off in easy of playing.
Race wise, it's basicly a toss up. I have a Draenei myself, and I wouldn't trade Symbol of Hope (SoH) for the world. That's alliance side. Horde side, I have no clue what is best.
If you play alone, you'll find it easier to play as Shadow as you level. Most priests level as shadow until around level 60ish. Then they will either continue as shadow if they intend to stay so at 70, or spec holy and learn to be a better healer before they hit 70. As shadow, things will drop like flies once you get Shadow Form. (that whole taking off at level 40 thing means this) All in all, you have to ask yourself what you want to do. DO you want to be the guiding force behind the group, making them stay alive in really bad situations where one mistake by you can cause the whole thing to come crumbling down? Maybe you want to give back to the group by dealing damage quickly, but having to watch how much you do else the bad thingers start to pay attention to you and you realise that silk blouses don't stop swords often? I prefer holy myself. I raid in end game content (really hard places with thingers that really hurt, all 25 of the players at once.) As OzoneSSX said, it is a very thankless job. Most people prefer to have either a Paladin or Druid heal a group of 5 people. Mainly cause there are a lot of bad priests. In the end, it's your game, so how do you want to play it?
As to the boring part of priests, it's far from so. Well, at least healing isn't IMO. Most other healers have 2 or 3 buttons they push. I have 9 buttons for heals. (yes, I use all of them in a run of something and only one is a downranked) Add in 2 for regen, 2 for "OH NOES!" times and 1 for dealing some damage. The thing that seprates bad priests from good priests is simple: We have many heals and they are all useful at some points, but not at others. Priest healers have to think as they do what they do, but keeping your 5 person group up is easiest as a priest, since you have so many tools to do the job. Toss in the fact you can react to things better (all those tools) and you have an intresting, involving and satasfing game play.
As to your professions, I'd suggest taking Herbing and Tailoring. You can make your own armor as Tailor, and herbing alows you to pick some flowers. Those flowers can then be made into potions by other players or sold for cash. As a starting player, you aren't going to have much money for a while, and these professions help to offset that a bit, without going for a min/max style of play. In the end, any combo works, as long as you enjoy it. Or you can go very strange and take Engineering and mining. Funny things happen to Engineers, but I won't spoil the suprises. ^.^
All in all, it's up to you. The best way to find your personal choice is to ask how you naturally act in real life. If you sheppard or help from behind the sceans, you'll do well as a healer type. If you like to use brain over brawn, priest is prob for you. Best advice I can give with out going into too much depth. ^.^
Linky to my toon: http://www.wowarmory.com/character-sheet.xml?r=Detheroc&n=Niveus
(might be PvP speced as I'm starting to enjoy Arena now)
Good luck to you and keep us updated on your progress! ^.^
EDIT: Added thoughts on Professions and the fact I'm prob Disc speced for PvP action right now.
Edited, Jun 7th 2008 2:07am by Sioniv