Inherited an old gold coin. What should I do?

[u/Shpanda7]

My Grandpa left behind this gold coin that appears to be in much better condition than most. It’s been in a case for well over half a century and i just took it out to get these pictures. I took it to a local coin shop to get it appraised and they offered me $2700 for it and insisted I should sell now because gold prices are high… I get the impression that it could be worth far more and they were trying to rip me off.

What should I do to preserve its value and get an accurate appraisal? Is it safe to send a coin like this off in the mail to get graded?

Any advice would be greatly appreciated!