Your question is a bit too broad to really be answered well. Which machine shop work are you wanting to measure? Connecting rod resizing? Bore and hone? Crank grinding?
For home engine work, I'd recommend:
1) I quality 0.0001" resolution micrometer set enough to cover up to 3" or so. This is for diameters-- crank pins, main bearing journals, valve stem diameter, etc. You'll want a depth mic companion to go with it.
2) A digital indicator also capable of 0.0001". This was formerly the domain of only test indicators that has very little total travel, but you can now get Mitytoyo digital indicators with a whopping inch of travel that will hold 0.0001". These are super useful as they can replace a test indicator for most purposes, so everything from flatness checks, runout, etc can be measured with a single indicator and a variety of bases and attachments. Not cheap, but considering how many tools it replaces it is likely a great investment.
3) Telescoping bore guage set. If you are skilled, you can make a telescoping gauge set and your micrometer work pretty well, but it's cumbersome compared to a two point dial or digital bore gauge. Expect sticker shock for a real bore gauge that will make the telecscoping setup look very appealing. A cheaper bore guage will cost less than a good micrometer and quality telescoping guage set, but you'll be glad to have the quality of the latter and with practice it will be surprisingly consistent.
If you are consistently working with any particular size hole (say SB Chevy rod big ends or small ends) I'd recommend large diameter plug gauges of the appropriate size. Easy way to go/nogo with high precision and they're surprisingly cheap. $12-$15 will get you a gauge of the stock piston pin size that's within 0.0002" of true nominal. This only works for hole small enough to find a ready made gauge, but plug gauges are a super cost-effective tool in terms of price vs precision.
Also, a caution about using 2d data to generate 3d conclusions. If you measure a bore in 3 or four places to "check the bore size" you have NOT measured the cylinder. You have measured circles that are slices from that cylinder. You measurements are not guaranteed to be concentric/coaxial to each other. With enough measurement locations you can have some confidence that this is mostly moot.