@jeteague - You are welcome. I am more of a tinkerer, and that guitar was my first which I got it for next to nothing. The only mechanical alteration I made was the frets, really, and I doubt I have the patience to do one "from scratch" either. Even with electronics alone you can have a field day playing around if you enjoy such things.
 
@gswitz - Drew has a huge point about a pre-made neck, and for a "first" simplicity is easier. Honestly, a pre-made through-body neck (such as a Carvin neck) may be the best starting point. It would yield the best play-ability and sustain (no neck joint), and allow you for any "body design" and electronics you choose. That would probably be the most simple and effective, since that neck by itself is "really it" for the guitar mechanically.
 
 

NT6 Neck-Through 6-String Replacement Guitar Neck - Carvin  269
Grover Original Rotomatics (102 Series) 3+3 Tuners, 18:1 ratio, chrome  262
Premium Wiring Kit for Gibson Les Paul Guitar, Long-shaft CTS pots and chrome Switchcraft switch  79.42
Golden Age Parsons Street Humbuckers, Bridge, Alnico 2, gold  60.97
Golden Age Parsons Street Humbuckers, Neck, Alnico 2, gold  60.97
 
Total: 732.36
 
I don't have a bridge yet. What other things will I need?

gswitz
I don't have a bridge yet. What other things will I need?

I was going to say tools, tools and more tools.  Then I saw the mention of the CNC machine.
 
So sandpaper should do it.
 

a bolt on neck will sound/feel nothing like a les paul.
 
a neck thru guitar,
will not sound/feel like a paul either.
 
if you really want something 'like a paul',
i'd look for a used paul.
 
nothing you can build, is going to come close to that feel.
 
that said, i love bolt on necks more than glue-in long tenon necks, at this point.
but it's an aesthetic thing, that should not be overlooked.
 

batsbrew
a bolt on neck will sound/feel nothing like a les paul.
 
a neck thru guitar,
will not sound/feel like a paul either.
 
if you really want something 'like a paul',
i'd look for a used paul.
 
nothing you can build, is going to come close to that feel.
 

 
I agree with Bat.  A friend of mine was looking to buy a new guitar and he was looking at Carvin's; one of the neck through's.  He had always wanted a LP, but said he felt he could get more for his money through Carvin.  He went with the LP and has been emailing me ever since stating that he is so glad he did.  I love Carvin guitars.  Having own many Gibson LP's over the years...if you want that sound, get the LP.  
 
Used deals are out there.  I was eyeballing a Black Studio for less than $500 (with case), with very little play time, just before Christmas.  

gswitz
NT6 Neck-Through 6-String Replacement Guitar Neck - Carvin  269
Grover Original Rotomatics (102 Series) 3+3 Tuners, 18:1 ratio, chrome  262
Premium Wiring Kit for Gibson Les Paul Guitar, Long-shaft CTS pots and chrome Switchcraft switch  79.42
Golden Age Parsons Street Humbuckers, Bridge, Alnico 2, gold  60.97
Golden Age Parsons Street Humbuckers, Neck, Alnico 2, gold  60.97
 
Total: 732.36
 
I don't have a bridge yet. What other things will I need?

You might already have these and not all of these might be necessary in your case, but here is some of my checklist that might apply:
 
vol pots
tone pots
knobs
switches
jack
jack plate/ferrule
wire
tuning machines
strings
bridge/tailpiece
string ferrules
string retainers
straplocks/buttons
 
EDIT: forgot the control cover

I'm going to build these, seriously I'll order a neck from Guitar Fetish for $20, machines $20 , bridge and Pups I have already from other upgrades. Finding the right can will be the tricky part. 
 

Hey Bo Diddley ...
 

 
Cigar box guitars rock. Bo used to build these himself.

Dang, I forgot how truly massive that body was. Quick cutaway on a band saw and you got the "Les Paul feel" right there.