Never heard of "Handy Backup", which is a huge red flag.
Backup is a PITA, but it is the single most important job we have as sysadmins. Exchange in particular is finicky and hard to do properly. I would be very hesitant to use something unknown or to go cheap on backup. Cheap is great until the server has crashed and Exchange on the new one can't load the restored data store. Then you have to be cheap because you are unemployed!
I recommend you use a server-oriented backup system (such as Backup Exec) for the servers, and another (perhaps HandyBackup to a NAS device) for the clients. There are lots of options .. get started with these questions for more info ( a b c ).
I also recommend that you start simple (daily to tape) and when that is stable get more complicated (disk-to-disk-to-tape, off-site replication, etc.). Test the backups by doing restores on a frequent basis, and have a tested, verified, up to date procedure for restoring each server from the backups.
I second Evan's Backup Exec recommendation. It isn't always easy to configure, but it works.