On the topic of marriage + permission to stay

Hello, and thank you for the time to read and respond!

I have met the love of my life, and she lives in Vienna, Austria, or as they say, Wien, Osterreich. I am currently on my first visit to Wien, but we're serious about marriage.

I have read that it is very hard to get Austrian citizenship, but, I am less concerned about that for now (being American), and more concerned about just being able to stay with her.

Things I understand about Austrian immigration:
* German speaking is preferred to get a permit to stay in Austria
* Skilled workers are preferred to non-skilled
* There is an expected monthly income requirement, so you don't use the welfare system
* It is becoming very difficult, if not impossible, to seek asylum

1) Thankfully, I am a computer programmer, and that seems to be an in-demand job out here, and in most of central Europe.

2)  I am financially stable, and make many times the noted monthly income requirement from work back home (my job is supportive of me being with this girl, so much, they're letting me work remotely!!!)

3) I am not seeking asylum, as I am marrying this girl, not running from any kind of a political issue back home

Regardless, I am asking what the best course of action to persue legally staying here....at least temporarily. The permanent citizenship status can come later, I understand, after I learn German and remain in Austria for a certain amount of time. That's not my issue yet. I just want to be able to stay with her, now that we're together.