Getting the backup schedule right

I'm revamping the backup schedule for the database. There are 3 different types of backups: Full database backups, Differential database backups (just the things that have changed since the last full backup), and Transaction Log backups. These each eat up a substantial amount of disk space, and have to be scheduled carefully so they do not interfere with each other or cause the disk to run out of space, as happened this morning while I wasn't watching! Getting this right will be one of the last major hurdles before I cut everything over to the new servers.