I would recommend LiPos rather than LiFe. As Lucy said, extra power and less weight. You have to take a few extra safety precautions in to account, but treat them with respect and you will be fine.
The flipside of LiFe batteries (and the main reason why I use them in my heavier robots) is that if they break, they are less likely to combust than LiPos. Perhaps less of an issue if you have in a metal box or, like I do, always have them in charging bags as they add some flame dampening.

As Andrew says, you do have to take some extra precautions as laid out in the rules if you use LiPos but TBH, its sound advice for any handling of batteries anyway. Its why I always include a fuse in my circuitry even if it wasn't required by the rules.

I recommend Robodojo Sportsman for your first few events as you will likely not take too much damage.
Gah, I can never get to a RoboDojo for it being on a Sunday. To be fair, Robots Live!, because they don't permit spinners, offers a nice entry into doing the live show circuit with all the atmosphere that comes with it. Dojo is a closed event, only open to Roboteers who pay to get in (the fees are perfectly reasonable). Both have their own pluses and minuses is what I am trying to say. :P