Long stay visa

Hey guys right here goes..

My wife and I would like to live in France.

We are currently living in Australia. I am a kiwi married to a french citizen.  We got married in Australia and have a daughter who is one year's old.  She was born in France.

We have just got back official documents of our wedding certificate from the French embassy,  I didn't quite understand this part but apparently our marriage wouldn't be recognized in France unless we sent these papers to the French embassy which we did.

Now I've never needed a visa before and struggling with this wizard visa on the website...

The link :

https://france-visas.gouv.fr/en_US/web/ … Model=true

You need a visa unless you are

and one of the options was -

> Family member of a citizen of EU/EEA/Swiss national (for the family member involved, refer to the section “your plan”, choose “family purpose” then “family of european national ”) and if you are exempt from a short stay visa for the Schengen Area.

*(or Iceland, Lichtenstein, Norway or Switzerland).

After clicking around and multiply windows opening I get lost...
I'm just puzzeled of what long stay visa is for me...

I'm even more confused as I was also told that I didn't need a long stay visa since I was married,  and have a daughter who was born in France and just to go the prefecture close to the area I would be staying in France and apply for a resident permit??? That would be able for me to stay longer.

It's doing my head in,  any help would be much appreciated. Thanks guys..