Do I append or overwrite?
If it's going to tape afterward I'd overwrite otherwise pick an acceptable on disk timeframe for the backups to expire (based on your recovery time) and append.
Do I set the daily backups to expire?
[Rackspace does a daily differential
and weekly full i believe as well]
Yes unless disk space is not an issue
Do I need to backup the transaction
Yes as frequently as you require for a point in time recovery. for example if your SLA says that you will only lose 15 mins of data in case of a failure you need to back up the trans log every 15 mins.
Do I need to shrink the transaction
No- unless you've somehow let it grow to ginormous size at one point and it never uses more than 1% now, and you are running low on disk space, then maybe
Please share some insights, best
practices. They'd be greatly
You need to work with the business to determine what type of data they expect to lose in case of an issue and how long then will allow the DB to be unavailable. Once you have the agreements on those in place the rest becomes a math exercise. In your example you mention that you do 3 fulls a day. You need to find out if that's just someones shot in the dark or if there is a reason it's 3 a day (maybe due to recovery times incrementals aren't possible)
Note that only after you get business requirements can you plan your recovery. The mantra of "plan your recovery" is so overused that many admins actually believe that and simply make the same types of mistakes they'd make if they just worried about backups.