Actually rooting the phone doesn't make the slightest difference to performance so don't worry about that!

Some of the advantages of rooting are:

1. Custom ROM's ( Flashing Aftermarket software which allows you to keep your software up to date when OS updates aren't available or just want something different )
2. Custom Kernals ( Allows over/under clocking of the CPU )
3. Remove Bloatware ( Delete poinltess apps that aren't usually available to delete )
4. Nandroid backup's ( Complete backups of everything on the phone )
5. Free Wireless tether
6. Dual Booting ( Can switch between multiple ROM's on boot )
7. GameGuardian/GameCIH ( Edit points or score in apps ( basically hacking apps ))
8. Freedom ( App which on supported apps allows free purchases from the play store )

When you are rooted you can do pretty much anything! Its gives you access to all the restricted things and allows you to change them at your will! The possibilities are endless!

As for the disadvantages:

1. Voids your warranty ( Phone can be fully unrooted so this doesn't matter )
2. You can brick your phone

Basically as long as you know what you are doing you will be fine! Keep regular Nandroid backups and you would be fine!

-Ben- has it right. But I'll add to it.

Before rooting your phone make sure you read all the instructions. The easiest way to do this is to find it on XDA. There you can find a tutorial as well as all of the necessary tools you will need. Rooting is not hard, but there is always a possibility that you might brick your phone.

As long as you read the instructions first and don't make stupid decisions such as trying to flash a ROM that wasn't designed for your phone you'll be ok.

SynergyEclipse wrote -Ben- has it right. But I'll add to it.

Before rooting your phone make sure you read all the instructions. The easiest way to do this is to find it on XDA. There you can find a tutorial as well as all of the necessary tools you will need. Rooting is not hard, but there is always a possibility that you might brick your phone.

As long as you read the instructions first and don't make stupid decisions such as trying to flash a ROM that wasn't designed for your phone you'll be ok.

Thank's for adding to my post! I should have put that in my original! There are was to fix bricking Samsung galaxy's so if you do mess up its not the end of the world! Everyone on XDA are extremly helpful and will help you sort your phone! I've been there plenty of times and people on XDA have helped me out a lot! There a quite a few member's on here who know there way around phones quite well also! I'm usually always lurking around as well and try and help out as much as possible so yeah! Have fun experimenting and if you need help Pm me or something!