By default Maya uses centimeters but there are several other options in the "Settings" category in Windows>Settings/ Preferences>Preferences, this sets it for the current scene. If you want to change the units for future scenes you'll create, check out the File>New Scene>options. As Stwert mentioned, there are snapping options as well, whether you want to snap to grid, points, curves etc. There is also a discrete feature that allows you to edit in increments when using any of the transformation manipulators, just hold down the "J" key(I'd say this is far more convenient than a checkbox in the tool's settings window), you can adjust the the increments by changing the "Step size" in said settings.

As for becoming O.K with being less accurate, that's tough spot to be in. I supposed you could remind yourself that as long as the model communicates the intended idea then you can move on.