SQL Server 2000 backup schedules

We recently upgraded to SQL Server2000 and the backups I inhereted were less than optimal to say the least. It basically is just a full backup every morning and evening and a few on the weekends.

I’m looking for some advice or even a 3rd party tool (if one exists) to analyze/optimize our SQL data backups, to create better, more efficient backups.

Or is a simple, periodic full database backup (full db, differential, & transaction logs) sufficient? And how often should this be done?

Any advice is greatly appreciated, thanks!