I would recommend you to begin with contacting NARA, after first reading the info in their below subpage regarding military records. As you are "next of kin", you have a right to retain copys of your fathers military records. What you should ask for, are copys of:
1) Your fathers DD-214.
2) Your fathers so called "201-file".
In the above, you will find Everything regarding your fathers service, e-x-c-e-p-t his medical records, which are kept separate. But everything else regarding your fathers military service, will be in the above 2 copys.
