Using Ola Hallengren's full backup but database option is for simple?
A full backup can be taken from a database in any recovery model (full, simple, or bulk-logged). It is an unfortunate conflict in terms that is somewhat overloaded. You could consider this type of backup to be a single, point-in-time, snapshot of a database that can be restored on its own in entirety.

The recovery model just dictates how logging works and whether log backups are possible.


In simple recovery model, you can take full backups and differential backups, but not log backups. This means you cannot restore to a point-in-time other than the time the any given full backup was taken (or that full + latest subsequent diff). It also means your log space is re-used because, once a transaction is committed, it no longer needs to be in the log in order to be backed up.
In full recovery model, you can take full and differential backups, but you can also take log backups, which allow you to restore to any point in time covered by any log backup taken since the previous full or previous full + previous diff. In this case log space isn't re-used until they are backed up, and most people find this out the hard way after the logs have filled a disk.
In bulk logged recovery model, the situation is essentially the same as full, except that portions of the log are "blocked out" - meaning you can't restore to a point in time that exists in any window where bulk operations that were minimally logged took place.


To summarize:


The choice between full and simple recovery model is impacted by your need to support point-in-time recovery (and is a choice that has nothing to do with whether you use Ola's solution to manage backups).
The choice between full and log backups in Ola's solution is clearer - you must use full if you want any backups at all, and you can additionally specify diff if you want, and log if you have databases in full recovery model.


There is a ton about recovery model and backup/recovery strategies online, I just wanted to clarify the difference between the two uses of the term "full" here.