I use the following Linear polarizers, no problems.
For some cheaper types of Auto-Focus, there were problems with Auto-Focus. However, in modern day, non-compromised auto-focus systems, you should not be getting problems with linear polarisers. The problem you might have, is a lack of light comming in, which would be the same with a CPL.
Quantaray LPL
Unknown Brand LPL - Made in Korea
Hoya Purple LPL
Jessops LPL
The mirror test will work, just make sure you turn it round so that you try it with both faces.
A circular polariser, is effectively two filters. It has a linear polariser on one face, and then a 'diffuser' on the second face. The second filter un-polarises the light.
For 'cheap' auto-focus systems, they split the beam and then re-combine it. IF the beam is only 1 angle of polarisation, there can be diffraction effects, which might effect the result. With a Nikon camera (don't remember seeing what it is specifically), I do not think you will have an issue.