"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 ??????/?