Standard micrometers (like those shown below) have a 25mm measuring range, so if you want to cover a large size range, you need several of them. They are graduated to 0.01mm, which in practice means that you can measure something to the nearest 0.005mm. If you want to measure this accurately, though, you need to make sure that your micrometer is correctly adjusted.
For the 0 - 25mm micrometer, this is fairly easily achieved. Make sure that the measuring faces are clean and undamaged and then close the jaws up. (Most micrometers have a ratchet mechanism so that a consistent force is used when taking measurements.) With the jaws closed, the scale should read zero. If it does, everything’s rosy. If not, all micrometers (when new!) are supplied with an adjustment spanner and instructions on how to zero it.
It’s a bit more complicated with the bigger micrometers as these obviously don’t close down to zero. In this case every micrometer (when new!) is supplied with a precision setting standard of a known length, to check and adjust the micrometer to. If you’re buying secondhand micrometers, these are often missing and as they are expensive to replace, budget for this when deciding how much to pay.
Micrometers like these can only perform external measurements. If you want to perform internal or depth measurements then you need an internal or depth micrometer respectively.
It is also possible to get micrometers that are graduated to 0.001mm. I’ve never seen one - they used to be extremely expensive - but (as ever nowadays) there are cheaper, unbranded versions now available.
For general bike work, you’ll probably only need a digital vernier. If you start doing engine work or machining, then you might want to look a micrometers.