Read Blazinzuk's post above over and over.
A half cab gives you a lot of protection to start with so you don't have to get as carried away with the cage as with a full convertible. Those B pillars in the half cab are pretty beefy as are the doors and windshield frame. Keep the windshield from smashing down too far, protect the back seat and connect the two and you're doing OK. The half cab is also good in that the sheet metal keeps you contained if things get hairy, it keeps stuff from getting in with you like a tree stump in just the right place, and it spreads point loads over a bigger area to some degree. There's a reason Ultra4 cars have at least a 1/8" roof skin fastened securely to the cage, along with window nets.
As someone said above; in a full body rig, a good roll will total the truck. If you survive this, you're good but no matter what you're chances of recovering more than a few parts are slim. I saw the full convertible K5 that rolled on the UA trip in '14 and it was ugly. The 205 was about the only part that was usable after the roll. Axles bent, engine parts and trans case broken, frame trashed, no good body panels. It fell over backward on a pretty steep hill and the cage barely did the job. It could have been built from bigger tube since I think a lot of it was 1.5" and it didn't have many complete triangles. With that same cage in a half cab the truck would still be totaled but he would have had a much bigger margin for error in surviving.
Dropping through the floor to the nerf bars is a good idea since it beefs up the nerf bars to where they become functional to hold the truck up and not bend everything and it also beefs up the frame and provides extra cage support.
There are a bunch of pics of my k5 when it was full body near the bottom of this page. I would consider this cage to be a good minimum with a half cab.
You can see the A pillar to nerf bar tie in the upper right corner of this pic:
That's a 2" tube on the bottom and a 1" tube that runs to the top of the frame. It was all bushing mounted which I would not do again since it doesn't do enough for vibration absorbtion to be worth the hassle and weak point.
This pic has a peek of the rear cage legs tie to the bumper outrigger on the frame:
You can see the bumper tie here also, along with the tabs that accept the bushing assembly for the B pillar tie that was being rebuilt and raised up before BlazerBash '02.
Obviously the rig progresses toward the top of the page but the main cab cage structure is still the same as I built in the full body half cab. Looking at the pics, if it had stayed a full body full convertible we would have added some diagonals in the B pillar bay and probably overhead in the A-B bay similar to what we did after the full body was cut off. Access was really good with the original cage system and the only real sticky point was headroom in the back seat was not good for adults. OK for kids but that was it. Frame stiffness was WAY better with even the basic cage. I went from tearing out body mounts and cracking sheet metal in the half cab to a pretty stiff overall chassis. Definitely good for long term recreational use.
One thing that makes me feel a LOT better about that cage was the rear upper corner to bottom-of-B-pillar brace tube. That one tube goes a long way toward keeping the B pillar upright and the C pillar from smashing down. It didn't dead end by very much, I couldn't get it perfect because of the body corner it dropped into but it came close to picking up the bar that ran along the floor pan to the A-pillar.