The Compiled Military Service Records reside at the National Archives. If he filed for a pension, those records should be here:

Library of Virginia
Archives Division
800 East Broad Street
Richmond, VA 23219
Telephone: 804-692-3888
http://www.lva.lib.va.us/

A database of the Virginia Confederate Pension Rolls:

http://ajax.lva.lib.va.us/F/?func=file%26file_name=find-b-clas10&local_base=CLAS10

The following site contains links for some of the VA regiments, but not the 60th; however, it does have links for regiments by the geographical location where a regiment was raised.

http://www.geocities.com/Area51/Lair/3680/cw/cw-va.html