So I am signed up to play my first RPGA game September 18. I've played 4E for about a year so far. I was a big Forgotten Realms fan in 2nd edition, not so much in 3.x and I'm only starting to look at it again now for 4E.
I try to strike a balance between a fully optimized character and one that's fun and interesting to play, and for my first LFR character I think I'm going to go with a Deva Invoker. My idea is that my character is a servant of Amaunator, and has been reborn in his service many times over centuries; he's seen Amaunator's transition to Lathander, and now back again to Amaunator. I'm going to go for a very "Old Testament", hellfire and brimstone (read: Wrathful Invoker) style character, not a preacher but a judge, who punishes the wicked. I think this fits very well with the flavor of the Invoker, the Deva and of Amaunator.
Now, having not played LFR before, I'm not sure if I'll get many chances to roleplay my character; I've heard various things about the lack of roleplaying or anything other than combat and I hope this isn't the case; I wouldn't waste time with meaningless interactions, but at the same time I think my concept will be very fun to play and will be an interesting character.
Am I worrying too much about details for my character that will never show up?
It really depends on who you'll be playing with, and in what context. If the DM and the other players are, on average, strong role-players and prefer that play style, then you will probably get a lot of opportunity to role-play your character. On the other hand, if most of the other players prefer to roll dice and kill monsters efficiently without much role-playing, then you will likely not get as much of a chance to show off your backstory.
On another axis entirely, if you are playing in somebody's basement and you can take five or six hours (or more) to finish a mod, then you will likely get a lot more chance to role-play than if you are at a con or game store and have to be done and packed up within a four-hour time slot before the next group arrives (or before the lights are turned off and the doors are locked).
Of course, even if your group's play style isn't very condusive to role-playing, you can always sneak things in now and then. There's no harm in over-developing your character, as long as you're having fun doing it! The best novelists know a lot more about their characters than ever makes it into print, and the equivalent is true of the best role-players. If you know more about your character than any of the other players or the DM, then you are doing it right.
Even if you play in groups where RP is minimal... just talk like Charelton Heston as Moses during combat and everythign will be fine. 
What Dan said about time constraints and the group/DM you find yourself playing with is right, but I however love it when I run across people like you in the community. Welcome aboard, and I hope you find enough character development and interaction to keep you interested.
Thanks
At the moment I'm still evaluating concepts, because I admit there are a ton of things I like to play and not enough time to play it. My home game I play a Dragonborn Fighter so I'm a little tired of melee combatants.
One thing I'm wondering though is what role I want to play... see, my gut feeling says to make a Leader since a Leader is always welcome at a LFR table; maybe I'm paranoid but I'm a little worried that I'll run into a situation where I have a defender or a controller, and there's already one or two at the table so my character is redundant. Somehow I don't see that happening with a Leader at all, since who doesn't like having extra buffs and healing?
Am I worrying too much about that and should I just make whatever I think will be cool?
Leaders are always welcome on any table. My only advice is build a leader who can act as a leader rather than a defender or striker. The party wioll thank you for it... especially for the buffs and healing.
I'm striving to have a couple of characters at each tier with the idea that I can drop in a character which can helps balance the party.
That being said, play whatever you enjoy the most...