First to answer your question the tolerance of a 1/1000 of  an inch  would be written as +-0.001 and +-0.005 would a half thousamth of an inch.

Also it is important to note that generally the term resolution is different from a tolerance a resolution is the decimal point that a dimension(a certain measurement of a part ex. 1.5 in length, 2.125 in diameter, etc) an so the resolution of the lengh in the previous example would be a tenth of an inch and a thousandth of an inch for the diameter also the resolution means something slightly different if its refereing to a measuring tool. When refering to a measuring tool resolution means the most accurate measurement displayed which with a micrometer could be anything from 1/1000 of an inch to half a millionth of an inch.

Tolerances for dimensions means how far from the goal dimension the actual dimension of the finished part can be, also this isn't always +- X it could also be +X or -X or +X -Y. Tolerance when refering to a measuring tool is how far off the actual dimension of the part can be from the dimension displayed by the measuring tool when used properly. I highly recomend thouroughly reading a precision measuring instraments and look up tips online or asking someone with experience with such tools. One thing I would highly recommend with tools such as calipers and micrometers is making the measurment with your eyes closed because you are going to have a tendancy to try to get closer to the measurement you want to see.

As for the tolerances needed for the machine parts

How precise you need to make the ways would depend of many factors such as:

1.How big the guideways are. The thicker the are the more rigid and more dampening they'll.

2.How much vibration is created from cutting(how fast is the motor running and much much material is it cutting)Also you have to take into consideration there is a variety of tolernces that affect accuracy.

To get an I dea of how accurate you need parts to be I would first figure out how far off the the dimensions of the finished part can be be from the goal. The tolerance should be 3 differnt ones(one in X one in Y one in Z) or distance goal XYZ point to auctaul XYZ point. Then your going to have to do some math and taking in all of your parts into account to figure if the majority or all of dimensions were off how far off in XYZ your cutting tool would be.

Here are some dimensions to be aware of beyond basics like lengt, diameter, width, height, etc.

How Congrument or Parallel a dimension or part is in degrees

How flat a surface is: this is generally written as the acceptable variance in height over a certain area, length, or entire surface of a part.