Seeing that the recovery model is set to simple and msdn states that the simple recovery model does not support point-in-time recovery - Does this mean that I won't be able to use my transaction log backups to restore the database in a disaster to an hour before it happened?
Even taking a transaction log backup is not supported for databases using the SIMPLE recovery model. This is a restriction of the database engine based on how this recovery model works, and the recovery features it doesn't support, as you mentioned.
A transaction log backup maintenance plan task automatically skips databases in SIMPLE recovery to avoid causing errors.
Which backup should be done first, the database backup or the transaction log backups? Articles that I'm busy reading say I should do the database backup first and then the transaction log backup else I will get maintenance plan errors, but I'm currently first backing up my transaction logs and then data databases and I'm not getting any errors.
For the reasons I mentioned above, it won't matter for databases using SIMPLE recovery, as they will be skipped by the transaction log backup task.
For databases in the other two recovery models, a full backup must exist before you start taking transaction log backups (just the first time), or you will get an error -- this is probably what the articles refer to.
Point-in-time recovery ability is normally driven by business need -- in other words, you determine how critical the data is and how much you can afford to lose, then set the appropriate recovery model to meet those needs, and finally create a backup solution.
Even though SIMPLE recovery does not support point-in-time recovery, if an hour of data loss is okay, perhaps a differential backup solution could work for you. (There are far too many variables that go into developing this kind of solution to give you a complete picture with what was provided in the question.)
I use Ola Hallengren's scripts these days to support some 50 SQL Servers. See: http://ola.hallengren.com/ and download his MaintenanceSolution.sql. These scripts have won several awards and are quite widely used.
The documentation is quite good, for guidance on backups and other database maintenance feature. You can choose frequency of backups, types of backups, retention of backups, and on and on. (In the past we used SQL Server's Maintenance Plans, then some of our own code, and now Ola's scripts.)
I have a one month retention of backups, some have more and some less. The backup retention period is specified in hours, not in days, so you do have a lot of flexibility.
One comment on deleting files is that you ideally should do each backup (or perhaps each day's backups) to an individual file. That way when you delete a backup, you only delete one backup (or one day's worth of backups.)
Best Answer
I would recommend you to study and implement Ola Hallengren's SQL Server Backup solution. Its free and is widely tested and recognized in the community.
e.g :
Back up all user databases, using checksums and compression; verify the backup; and delete old backup files
Automate and Improve Your Database Maintenance Using Ola Hallengren's Free Script will give you a good start.