The other answers discuss mounting the drive directly. However, given the age of the disk and the stated personal value of the contents, I would like to recommend that the drive be imaged first. GNU ddrescue is your friend.
ddrescue will create an image of the drive which you can then mount and work with. This way you only have to connect the drive once ...
I had to add the sizelimit option with the partition size to make it work, so as in your example:
sudo mount -t affs -o offset=,sizelimit= /dev/sdc /media/Amiga
And if you also want user access and not just root add the setuid=,setgid= options as well