Request an owner's manual from Ruger on their web site or take it to a gun smith.
Ruger's website has extensive sn data.
100-500
Depending on condition, and WHICH version of the M77, between $250 and $500.
Unknown caliber. Contact Ruger
If the Ruger website is up, it has sn data.
The Ruger website, under customer service, historical data, rifle, M77, will have the serial number ranges for each year of production.
100-400
Remington 700 308?
50-700 usd
Long
Strong enough for factory loaded ammunition and hand loads that don't exceed SAMMI standards.
You can request a owner's manual from Ruger at their web site.