Below is a photo of what I use for removing the primer crimp from .223/5.56 cases. The Hornady Case Prep Center has three tools, in the rear is a VLD deburring tool that I use to remove the majority of the crimp. I then switch to the top tool a RCBS crimp reamer for their case prep station. The RCBS reamer removes the rest of the crimp, I then use the Lyman crimp reamer as a GO NO-GO gauge to see if the primer pocket reamed enough.
The problem with the Lyman type reamers is if the case is tilted you will score the primer pocket side walls and remove brass.
I prefer the RCBS reamer below because it is tapered and will not touch the side walls of the primer pocket. It will bevel the primer pocket and the face of the tool is the stop.
That being said the Hornady reamer below is sharper than the Lyman reamer
Hornady Primer Pocket Reamer Tool Small
http://www.midwayusa.com/product/501588/hornady-primer-pocket-reamer-tool-small
The problem with hand reamers even powered by a drill is the hand that holds the case gets sore when doing large batches of cases. I like the RCBS reamer but it requires more hand pressure than the Lyman or Hornady reamers.
The best unit is the Dillon super swage but is the most costly and since you have the Lyman crimp removers start with them. I would recommend thin work gloves to ease the strain on your fingers.
I got lazy and now buy 500 pre-processed military Lake City cases at a time that are cleaned, polished and with the crimp removed.
At the link below are more opinions, markm runs a AR15 training school and Molon has more money and doesn't get sore hands and fingers.
.223 Brass and Removing the Primer Crimp
http://www.m4carbine.net/showthread.php?185899-223-Brass-and-Removing-the-Primer-Crimp