LiPos traditionally require greater care than NiMH to be used safely. I say traditionally because they are in fact perfectly safe if respected. You would need a charger capable of balance charging LiPos and you need to put them in a fire retardant bag to charge safely (readily available, search LiPo charging or protection bag). I believe the current ruleset doesn't require you to have metal under the pack, it's a recommendation.

The advantages are in bang for buck. LiPos are miles ahead of NiMH in both power output and capacity per gram for the same sort of money.

That said if your robot doesn't require the huge power LiPos can put out then you may as well use NiMH for now. They will make a nice upgrade later on. Meanwhile you can read up about them and how to treat them; everything you need to know is online.

I wouldn't recommend really really cheap LiPo packs (Hobbyking's Nano-tech and Zippy ranges for example), whilst popular they often perform under their supposed rated output. I have used regular Turnigy packs (also Hobbyking) and have found them to perform well, would recommend. The best for roboteers are probably Optipower batteries. I think FRA members still get a 30% discount with Opti making them competitively priced despite being high end.

A good first charger would be something like the Imax B6. You'll need a suitable power supply for it. Cheapest place to get a B6 is you guessed it, Hobbyking!