Man, I can only imagine how many heads will turn when you get this car done! And I'm VERY familiar with one thing leading to another. I once posted a picture of my 81 before I started and called it a "bankruptcy starter kit"!
I don't know if you have seen my thread called "Another LS3 - T56 Swap into 1981 C3" but it has several things you might find of interest. I highly recommend removing the body if you have means to do so. Cars this old need lots of love and it is light years easier to do when you can get to everything.
Since you mentioned lifting the body, here I go again with a few suggestions! First, several places sell straps with a "hook" on the end of the strap. There are 4 straps. I'll get straight to the point: I do not like the straps AT ALL. They would probably be ok for just a quick lift to take care of something but they are not suitable (my opinion) for any kind of restoration. Here's what the straps looked like in action. The body sways uncomfortably if you try to do much work on it.
So, I fabricated 4 lift "buttons" that would fit each of the lift arms. The "blades" will fit between the frame and the rocker panel. Here's what they looked like before I welded them together. While I was turning the "buttons" I went ahead and made 4 extra in case I have need for them in the future.
Here's what they looked like after welding and paint. The "button" was designed to fit into the hole on each of the lift arms.
And, here they are in action.
The bottom view.
These are FAR superior to the straps and are a necessity (again, my opinion) for a thorough and safe restoration or service. They are not difficult at all to make if you have access to a lathe and a shear. If you don't, they are pretty simple and can be made at your friendly local machine shop. I doubt the cost would be prohibitive. I have drawings of the lift adapters to share, you would just have to make sure the diameter of the buttons is sized to fit your lift. Meanwhile, here are a few things good to know.
Be sure EVERYTHING is disconnected before lifting the body. Take your time and talk a friend into helping look for that missed cable or something. If the body hasn't been off recently they will usually try to stick a bit at the body mounts. But don't force anything.
Regardless of the body lifting method, it is highly recommended that you support the "nose" of the body by some method. If you search this forum and other places you will find a variety of methods to do this. Since I was going for a total rebuild, I went ahead and removed the headlight assemblies and just about everything I could remove from the front nose and fenders. This made the nose light enough that support was not necessary.
There are 4 body mounts along each side for a total of 8. There is a ninth mount right at the nose of the car that bolts down to the "crash bar". Don't forget that one! And when you start looking for the replacement of that front mount you will have a little trouble finding it. Fear not though, it is identical to a C2 body mount.
Avoid excess lifting or pushing the ends of the body while it is on the lift. It's just sitting there, not secured. I didn't find that to be a problem, but stop and think before crawling inside the cabin. If you go all the way to the back the body will endo. Again, not a problem, just remember the body without the frame isn't really all that heavy.
NEVER attempt to lift the car using the body adapters with the frame attached. You will seriously damage the body.
The body is a tight fit clearance wise to the frame. It's easy to snag something when setting the body back down on the frame. Here's a tip. On the driver's side (US drivers) rocker panel, a little ways back from the door hinges, you will see a hole in the rocker panel that goes straight down. You may have to remove the plastic cap plugs if they are present. Likewise, on the passenger side rocker panel, near the rear you will see a hole that goes down through the frame.
Get 2 metal rods about 12" (305mm) long and a diameter of 7/16" (0.4375") (11.1mm). When it comes time to remount the body, drop one of the rods in the hole near the front of the driver side rocker panel, and the other rod in the hole near the rear of the passenger side rocker panel. Use a clamp or something on top of the rod so that they will not fall all the way through the rocker panel. When you lower the body, the rods that are hanging out of the rocker panels should be aligned with the corresponding holes in the frame. No guesswork. That's how the factory did it. Once the body is placed to your satisfaction pull the rods out and that's that.
Hope I didn't swamp you with too much information again!