There are no cons to rooting your phone, unless you do it wrong and brick it. If you don't know what 'brick it' means, it's exactly as it sounds. Making it into a useless brick that will never work again. I'd defiantly read up on a few tutorials and see if you feel comfortable doing it. It's not hard, it just involves doing things that are going to void your warranty and ruin any chance of having it replaced if you do mess something up.
http://www.xda-developers.com is going to be your best friend in this journey.
EDIT: You can unbrick a phone in some instances, so don't take that to serious, but it's rare that you brick a phone just rooting it. It's usually flashing a new OS variant or special mods to it that will brick it.