Starting out in FFXI, it's hard to be "unique" since there's only 5 races, 8 basic jobs, and hundreds of thousands of players.
The uniqueness comes in more 1) when you get your sub/adv job 2) when you start getting specialized armor/weapons/toys and 3) when you develop a personality for your character.
1) (warning: math ahead) There are 16 different jobs, each with 15 different possible subjobs, for a total of 240 different "combos". There are 8 race/sexes with 5 faces, 2 hair styles, and 3 sizes, which makes 240 different "templates" for the characters. That means there's a maximum of 57,600 "unique" characters available in the game. Since there's (unofficially) 400k users or so on 20 servers, there's around a 40% chance anything you pick will be duplicated on your server somewhere (some combos are obviously more used than others).
2) (no math) I don't even know how many different types of armor combinations there are, but while everyone in the lower levels will look pretty much the same, when you hit the 20's things start to differentiate between classes, races, and individual preferences.
3) Obviously, how you play makes you unique and is the most important factor in the game. It is, however, also the most important factor in differentiating you from other people; your personality (real or fabricated), your methods, the quests you've completed, your goals - all these create a unique representation. Do you craft? Do you do all the quests you can find? Do you just hang around the outpost helping noobs because you like watching your sword swing for 150 DMG?
Don't worry so much about the initial nature or physical appearance of your character; realistically speaking, it's going to be duplicated somewhere. Stay away from some of the more popular physical types, but more important is how you play. As for jobs, you can change those in-game pretty much at will, so if you try something and decide it "doesn't fit", just change to something else.
Good luck with it!