It sounds very similar to our situation in Calgary where migration is excellent, inventory is abysmal and new growth sectors are emerging.

If you are concerned about price points and current valuations then you need to find an emerging market where you can achieve a bigger bang for your buck.

If this is a real emergency situation I can allow it and start looking for a new tenant, but is it appropriate to ask for any medical papers?

Or an emergency.

We mostly intended it to be a capex emergency fund in case we have something big and unexpected come up.

In Texas providing hot water of at least 120 degrees is required by the property code, and any failure of the system would be considered a health and welfare issue and an emergency.

If it is not an FHA, you will likely need 20%, closing costs + emergency fund.Is it worth investing outside of your state?

I have the capital for a down payment (without touching my emergency savings), but I don't know enough about investing to buy a rental property on my own.

Our banks require we put up a sign of who is handling the property, for emergencies, etc.

Why not save for a little while longer to give yourself a personal emergency fund (6 months worth of personal expenses is a good place to start) and then pull the trigger on the next property?