What are the best financing options for this?

I believe, aside from house hacking, a LTR as your first investment is a great option since it will teach you many different aspects but not deal with the headaches of a STR. 

Look for other types of renters who aren't necessarily affiliated with hospitals or go just outside the neighborhoods immediately surrounding the hospitals and market it as a good option.

You may be able to find a value-add property there that gives you an equity option in the short term.

Think if there are other options. - I do not think you will hit your $70k target unless you get an assist by appreciation.   

What are my landlord options? 

You are missing out on an opportunity to train your inherited tenants to pay on time (and potentially extra revenue) by not using an online rental payment option where you can automate your late fee collections.

There's still some affordable options in the area. 

What would be some options for us?

House hacking isn't an option for me, unfortunately, so the BRRRR method is what I'm considering.