You should have two separate plans, one that does full backups and runs however often is required for full backups and a second plan that does log backups and runs however often is required for log backups, usually a lot more frequently than full backups.
The integrity check (DBCC CheckDB) should be run before the full backup preferably.
Gail Shaw
Microsoft Certified Master: SQL Server, MVP, M.Sc (Comp Sci)
SQL In The Wild: Discussions on DB performance with occasional diversions into recoverability