tool for measuring neck width and depth

Vernier, dial, or digital. Any cheap 4" or 6" set of calipers would be fine.

 

Calipers are your friend - If you want to measure the thickness with the strings on get a small block of known size to get your calipers over the strings - (measure it with your new calipers ) - then take the measure and subtract the thickness of the block. You can go up and down the neck like this and easily get the data you're after. If you have a decimal caliper just lay it against a ruler. I have both decimal and fractional now and use both extensively. One thing I've learned about working on guitars - measure, measure and measure some more and write it down!!! Saves me a whole lot of swearing later

 

I use an old micrometer, from my tool-and-die days.

 

Yeah, but it's hard to accurately gauge the depth with them...

 

I picked up a digital caliper at one of the big-box hardware stores for around $30. I use it ALL the time. A GREAT investment, if you're going to do much guitar work. I can't imagine being without it.
Just as a FWIW - I scrimped and got the plastic version, vs. the steel one - saved about $10 or so. But if I had it to do over, I'd get the steel set. I had no idea how much I'd actually use it, and it's starting to wear some. Eventually I'll wind up having to get another one, and will not have saved anything. Just my $.02....
El Steve-0

 

Spend a few extra bucks on a set of Brown & Sharps dial calipers. They rule the caliper/micrometer world, IIRC. I have a couple of B&S, and a Mitutoyo or two, and the B&S have much better "action." Also, the dial calipers are so much more friendly, once you get used to them.

rooster.

 

I think Mitutoyo/Starrett/B&S would probably be overkill if you just want to measure a neck. One of the knockoffs would be fine. Not saying you shouldn't buy a really nice one, just that it's not needed. Nice tools do feel good though. Solid. And you know you'll never need another one.

 

Vernier calipers will work, but if the jaws are short, sometimes it can be hard to get an accurate reading.

I like a transfer type caliper:
http://www.generaltools.com/Products/10-Outside-Caliper__452-10.aspx

You can use it to get a measurement in the center of the back of the neck, or even off center to get a feel for the profile - and you can get measurements with the strings on