If you're going to use a router, you need a 1/2 inch shank, not a 1/4 incher. I also like having a bit with interchangable bearings is a real bonus. I always prefer to use a router table for such cuts because it is very difficult to hold the router stable on an edge even with an edge guide. I also like using a table saw for this purpose, very fast, and you can do it with any blade that gives you a clean bottom. Even with a coarser blade, you can always smooth the bottom of the rabbet with a plane.
The more I do, the less I accomplish.