"The Cab shows an R55" on the front inward curve and on the top arch. What exactly does that mean? I'm guessing the "R" stands for Radius, and the arch/curve represents the outside edge of a 55" radius circle?"
Yup, you got it.
"If so, ok, so I can create the arch using a make shift protractor of string and a pencil secured to a center point. Where do I place the center point?"
Actually, you'd be making a drawing compass. Protractors are the things you use to measure and mark angles

Here's what you do once you have a compass set to 55 inches:
Set the anchor at the top of the side panel where the edge of the R55" arc is, and mark an arch at the bottom of the cabinet. Do the same thing with the other "corner" of the arc. Place the anchor where the two marks you made cross, and draw the arc between the two original anchor points. Not quite sure how you would make the R40" or the other R55" since your center would be floating in space. Best bet would be to make a template or something with the arc top arch and copy it to the front side.
"Best way to cut it? Just use a jigsaw?"
A jig or bandsaw would be the best way to go. If you don't trust your saw skills, get it close and sand it the rest of the way...You need a jig to use a router like this, so you'd have to make a jig with a band or jigsaw anyways. (Fish...cut bait...fish...cut bait) Once you finished a side, you could probably use a router to cut the other side using the first side as your jig, so to speak. You'd have to have a pretty long bit though, depending on how thick the side panels are.