Michael, welcome to the forum. You will get a lot of very good advice and help here.
I'll make a couple of very humble suggestions. First, get a copy of Melvyn Hiscock's book Make your Own Electric Guitar. He covers both building from scratch and assembling a kit of parts as you are doing. He has a very good chapter discussing geometry that should help you understand the neck angle, as well as chapters on finish, wiring, fretwork, etc.
Second, find a set of plans for a LP Jr - a google search should turn up several sources, if not some of us can help. Plans will answer a lot of questions - how much does the neck stand proud of the body, what is the angle, what is the height at the bridge. Compare these to your parts and you'll see what needs to be done (if anything).
Next, get your hardware - particularly your bridge and tail piece. At least get their dimensions (suppliers like StewMac often have a spec tab). I'm assuming you will use some sort of ToM bridge - build a mockup to simulate its height at the lowest and highest adjustments - you will want the plane of the fretboard to be close to the lowest. Clamp your neck in place and put a straightedge on it to simulate the strings - make sure you are within reasonable adjustment (note that string tension, nut slots and neck relief will affect that slightly, the important thing is to be able to adjust action within those parameters). This is the set neck of a semi hollow body but the principal will be the same for your Jr. The little pieces of wood under the bridge simulate the studs, the blue tape marks the scale length
Find build threads where people deal with these issues. I've done several LP style instruments and have published threads (other forums). You can learn a lot from the way others have done things (and their mistakes LOL).
Lastly, even tho what you are doing is building a kit, if you have specific questions take them to the Electric Guitar subforum. You will get a lot more response and I think it is fair game to ask there.
Good luck, enjoy, and ask away