Lots of great advice posted here! For my part, I do think elves are the hardest of our races to RP really well, but also some of the most rewarding. There's something about their nobility, their near-eternality, and their undercurrent of tragedy that attracts many of us on a deep level. When done sloppily, elves are the most likely to be boring, silly, or flat-out ridiculous. When written with love and care, they can be fantastic. You get what you give to them.
For a first elf, I would very much advise picking a youngster, one who hasn't seen everything and been everywhere already. There are two reasons for this - the first is strictly practical. As an older elf, your character will be expected to KNOW all the history and the battles and the names of all those pesky kings and queens and their nephews and their second cousins. If your character knows a lot more than you, you may run into trouble pretty quick if the conversation turns historical!
The second reason is a bit more artsy-fartsy character-oriented. Realistic flaws must be a part of every 3D character and it's hard to develop a realistically flawed elf. So to summarize what I just posted in another topic, by playing an elf, you are already eliminating all of the obvious possibilities for weaknesses that you might have as a mortal. That'll force you to go deeper into mental or spiritual weaknesses. But the older the elf, the more time they have had to 'figure out' the world and their place in it, so many many more possible flaws go out the window. For that reason alone, young elves are far less susceptible to Perfect Character Syndrome. Perfect characters are never good ones.
As others have pointed out, the road to originality lies in the mundane! We've seen way too many half-elves, elves in love with men, elves related to famous elves, and elves whose father was Elrond's long-lost third twin. That kind of stuff seems at first the most obvious way to spice up an uninteresting character, but don't be tempted! Besides the lore issues, off-the-wall backgrounds are often newer writers' ways to attempt to make their character more interesting. I know from experience that you are much better off starting with a very ordinary background and building a really three-dimensional character to live in it.