All rooting does is give you then option to allow apps to have lower level control to the device, there are no inherent benefits to rooting. The device works just as well as it does without rooting.
Once rooted though, root apps are allowed to do more on the device than before.
TiBu was mentioned already.
You don't NEED to be rooted to install CWM, TWRP or custom recoveries in general but to install them from the phone via ROM Manager or Goo Manager you would need root. You can always push them manually.
I'm a fan of Ad-Free which blocks ads from the device at the network level, so it applies to almost all apps.
I like root explorer, it's just a root level file explorer.