The command for giving everyone read-write-execute access (as you tried with the chmod) would be
mount -o umask=000 /dev/sdc1 /usb
A better way for doing this is adding the line
/dev/sdc1 /usb vfat noauto,user 0 0
. You can then simply mount /usb
as a normal user (and you'll own everything in /usb).