You can use NFS or CIFS (through Samba), it all depends on what level of user access control you want and which user you want the files to be read/written as.
NFS will try and use the uid/guid of the logged in user on the client machine, whereas CIFS/Samba will use the uid/guid of the server side user credentials you specify when you mount the share.
There isn’t really a native protocol for Linux. Both SMB/CIFS and NFS are supported in the Linux kernel. However, NFS is more preferred on Linux systems.
If you installed the App store version all automounted drives under /media wil be shared as an independent share. When you access the OSMC box you will see the “osmc” share as well as any other automounted.