If you really want to be a FI then you should go to a ATO that has a good reputation. Those who seek the cheapest usually finish up spending the most! When you go for a FI post, you may well be asked where you trained, if the school has a good reputation, that will be a help, if they have never heard of it, you are an unknown quantity irrespective of whether that school gave you your first job.
The standard of students arriving to do FI courses has fallen in recent years, no doubt due to the unequal standards that now prevail!