Your remington model 700 which has a letter A prefix to the serial number,indicates that it was made in 1980.
The C prefix to your serial number indicates that your remington model 700 was made in either 1982,or 2008.
Check the manufactured date link on the Remington Society of America for details.
The C prefix dates your Remington model 700 to the year 1982.
Only the 700 VLS is made in 6mm
You can't get type (possibly but I doubt it, even from Remington) for a date see related links.
This will tell you how to look it up. http://remingtonsociety.com/rsa/questions/barrelcodes
I don't know it that list exists but you can tell from the barrel code the month/year. http://remingtonsociety.com/rsa/questions/barrelcodes
You can tell the year by looking at the Manufactured Date information on the Remington Society of America - see related links. Later half of 70's they started a letter prefix but that's a 5 year window the date stamp is month/year.
The Letter actually give you a 5 year window, but the date code on the barrel gives you month and year ;) Check related links for information on the Remington Society of America for the details.
Since 1921 Remington has date stamped the barrel you can find the details/table on the Remington Society of America under the Manufactured Date link.
Your remington model 700 was made in 1982 with the letter C prefix to the serial number.