Long term investment plan for my kid's future?

[DaSpade]

She's less than 1yr old and I would like to see her financially secure to a certain extent when she turns 18 or so.

-I'm a total newb regarding investing.
-Would like to start off with $5K in her name.
-Will fund her account monthly upto $300 and will be untouched.
-Tax benefits(USA), would obviously be helpful.

Please let me know if I need to consider any other points.
Also, if this topic has been posted before or you could point me in the right direction, I would greatly appreciate it.

Thanks.