SQL Server – Are Non ‘Copy-Only’ Full Backups Safe for Recovery?

By "log shipping" I'm guessing you're meaning log backup? Log shipping is a high availability strategy.

If your full backups are taking the better part of a day, yes I recommend that you switch things up a bit. But that all depends on a lot of environment specific parameters. For instance, do you have a big window on the weekend where you will be able to do a full backup without interfering with users? (If not, you may need to look into filegroup backups)

A full backup once a week, and diff backups daily (again, in a maintenance window) is pretty common. As for your t-log backups, you need to determine the maximum amount of allowable data loss. In other words, if you back up your transaction logs every 30 minutes, you will have a maximum of 30 minutes data loss if the tail of the log is corrupt and unrecoverable. So determination will need to be made for transaction log backups.

(P.S. If you actually did mean Log Shipping then please clarify and I'll rework this answer. But by judging by your question I am assuming you just mean log backups)

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.)