The database size will increase rapidly if you have a LOT of mailboxes in one store and you do not set quota limits on the mailboxes. When planning an Exchange 2007 mailbox server you should plan for no more than 60 GB per mail store for optimal performance. To achieve this you have to set mailbox size quotas. That will ensure that the database will not grow beyond the size you have planned for. If you allow 1GB mailboxes then do not put more than 60 mailboxes in a store. If 500MB, then no more than 120 mailboxes per store, etc. Also you should consider implementing retention policies so that mail older than say 2 years is automatically deleted by the exchange server, or mail in the deleted items older than 30 or 60 days is automatically deleted.
As far as backing up exchange, that is something you will need to research in detail to find the method which best works for your organization. We use Symantec Net Backup, but will be moving to Tivoli Storage Manager soon. It’s all in the planning and storage availability as well as the cost factor especially in these times.