The full disk backup will only work if you are doing a cold backup (with MSSQLSERVER service stopped. The critical files to restore are master.mdf, mastlog.ldf and whatever files make up your database (select * from (dbname)..sysfiles) Getting back a database this way is a little tricky, as you will have to fool SQL Server into thinking it is still on its old home (SQL Server does not like machine name changes).
I would advise using any number of hot backup utilities. Most vendors (Veritas, OmniBack, Legato, etc.) have a plug in that will handle the SQL backups and restores.
You can do a full disk backup, but then you will only be able to restore to the time of the backup. If you use SQL Server to backup database and logs to a separate platform (preferably a remote location) you could do point-in-time restores up to the time of failure.
Can you afford to lose a day's worth of data?
For a single SQL database 3rd party backup tools should not be necessary, unless you already have some for Oracle which will handle SQL Server. You should get a SQL Server consultant to come in and analyze your situation to devise backup, restore, and secury procedures.