If I have a full backup scheduled at 6pm and a scheduled transaction log backup begins during the 15 minutes the full takes to complete, how would I use the transaction log backup during a recovery sequence?
Does the transaction log backup contain transactions that are captured in the full recovery since they both occured concurrently? Using RESTORE HEADERONLY I see they both are stamped as finishing at the same time.
Would I restore the full and then restore this tran log backup or go to the next tran log backup?
The rule is that tran log backups can only apply to the previous full backup. You should adjust your tran log schedule so that it's not running while the full backup is running. Your tran log backp, the one that finished 'at the same time' as the full backup is of no use. However, if you use Enterprise Manager and go throught the Restore window and show history, you can see the sequence of tran log backups relative to the full backup.
If you use Maintenance Plans, you can create a backup plan. However, if you decide to do it yourself using jobs, dump devices and so on, you will have more work on your hands to sort it out correctly. I personally think the extra work is worthwhile expecially for important systems - the ones you can't afford to lose.
My advice is to understand these issues very clearly and do some test restores into another database using differing database recovery scenarios.