Converting from 6spd downtube shifters to 8 spd brifters.
 

I'm only going to use a brifter on the right side/rear cogs, and keep the left side downtube. As far as I know, the only upgrades I'll need to do:

1) 8 speed brifter
2) 8 speed rear derailleur
3) New rear wheel with 8 speed compatible freehub (going to get an entirely new Neuvation wheelset, I think)
4) 8 speed cassette
5) New chain (about time, anyway)
6) New shift cable/housing
7) Cable stop
8) Time and labor

And I've got to measure my rear dropouts to make sure they'll fit an 8 speed system...what size am I looking for?

Anything I'm missing?

*maybe* new handlebar tape. Unless you take the old ones out cleanly.
The left brake lever will have to be adjusted to the same height as your right one.

Well, yeah, new handlebar tape. I've already got an extra pack.

Would it be easier to convert to 7 speed, rather than 8 speed?

RDs as a rule aren't picky, so odds are you won't have to replace it.
There is a 8-spd freewheel, which might be OK if you're not in the habit of bending axles.

7-spd freewheels are still easily available, although brifters are getting sparse.

For 8-spd you're looking at 130 mm o.l.d., or 135 if you're looking at mtb/hybrid standard.

even if your ride is 126, you can generally squeeze a 130 hub in there with no problem. ...although IIRC, some ppl say that if its an aluminum frame, that might not be so good??
I think your current 6speed is a freewheel and not a cassette. I guess this doesn't matter since you are getting a new set of wheels. You'll probably need a new chain to accomodate the 8 cog spacing.

You can pretty much use any shimano derailleur as long as it isn't pre1997 duraace?? I have a first generation 105 with a 9speed setup and there is no problem at all.

Regarding wheels and hub spacing: read the Sheldon Brown article on frame sizing, specifically the section on "Frame Spacing Adjustment."

Your current biking likely has 126mm rear hub spacing, and 8,9,and 10 speed hubs have a 130mm spacing. Read the article to help you figure out if its possible to get your bike to work with an 8 speed hub.

Other than that, your list looks pretty good. Good luck with your build, going from downtube shifters to brifters is a huge jump in ease of riding.

What kind of bike and components do you have now? Sometimes there's an easier fix. Some Shimano Uniglide hubs can be upgraded to a hyperdrive 8/9/10 sp hub for very little money. That could save you a new wheelset. The extra bucks could go toward buying a complete set of brifters.