"nothing is better than giving a trail"
try this iam also not sure
give DBCREATOR in serverrole and db_backupoperator in database role
normaly bulkadmin and public are common to non sysadmin
check in this
http://sqlserverpedia.com/wiki/Built-In_Server_Roles_%26_Database_Roles
and one doubt why are u giving the non sysadmin [is he/she also a DBA ] these backup and restore previllages ??????/?