You are
a chess pawn.
I'll go first, I'll lead the way
The pawn usually moves first in the game.
With some careful planning we'll make them pay
Chess is a game of strategy.
There's an incessant ticking off to the side
Don't take too long, you cannot hide
The chess clock is constantly going, and will run down if you spend too long on your moves. "You cannot hide" might refer to the fact that all moves are visible to both players.
I see others standing tall
I'm just as strong even though I'm small
The pawn is the smallest piece on the board, but it can still capture other pieces, even a queen.
If I should fall onto my face
I know another will take my place
There are plenty of pawns.
Our goal is in sight, I can see the crown
A little more time and we'll knock it down
I made it this far and you stuck with me
The reward for long life is royalty
If a pawn reaches its goal at the end of the board, it could gain a crown and become a queen.