Dimensions are usually interpreted by 3d printing software(slicers) as well, so you have to be careful to make sure they are correctly imported to whatever software the models go through before printing as well.
In Blender scene units are set in the Scene Properties tab in the Properties Editor:
Blender stores coordinate values in 32bit floats and the precision of numerical values in Blender as in all CG software(CAD software often uses more precise 64bit floats) is not infinite so for 3d printing it might make sense to change unit scale to millimeters so you can work with small values with no problems. Centimeters would work absolutely fine as well. You can see millimeters set up in the picture - unit scale set to 0.001 of the default unit that is 1m in Blender.
If you wish to always have the same settings when you open Blender, you should set them up in an empty scene and save it as default scene choosing File -> Defaults -> Save Startup File:
Note that other software likely will not recognise the units by default and you may have to set them correctly when you import your 3d models from Blender to it. How you do that depends on that software and you should refer to its documentation to find out how it works.