for .001, +- .001 with a .0005 repeatability, a good pair calipers is fine (see the mitutoyo 500 series absolute calipers
here )
IF you NEED better than that (aka Tenths), get a good mic - NOTE, you DON'T need anything near as fancy as the QuantuMike - nice as they are
You don't mention what range of sizes you're after, but on a budget, and assuming a somewhat reasonable range
1)A pair of good calipers
2)Mics of the appropriate size range - .0001 reading - watch carefully, they can run you less than $25-30 EACH, and remember you'll need one for each 'inch' you want to measure
3)A set of good telescoping gages
4)The expansion gages that are used on the sizes smaller than what the telescoping gages go (if you need to go down there)
That said, I'll give you my usual comeback to someone who says "Oh, I work to .0001" - My comeback - "Wow, who you using for your climate control system?" - if they can't answer THAT question, they are NOT really working to "a tenth" - Just remember that the coefficient of thermal expansion of Aluminum is 23x10e-6/degC - basically saying that a 3/4 aluminum tube/bar will change almost .0001 for a 10 deg C change