My suggestion is to make sure it's a house that other students will be in line waiting to help you keep it rented when/if you move on to another area, or town, and one that is very close to campus (walking distance is often optimal, but not an absolute necessity) might be helpful, but I believe making it an attractive-to-students house is important.... 

If there's a city that is trending toward 20%+ population growth over the next 10 years, especially in an optimal demographic mix, that's a pretty safe bet for solid appreciation.

Those alerts can also be seen if you mouse over the "Inbox" on the upper right menu bar and scroll down.

I had to spend extra money to make repairs, replace tenants, raise rents, and get the property at a optimal condition before I saw my first positive cash-flow.

Make sure that the firm you talk to is also competent in tax optimization as the structure needs to meet both asset protection and tax optimization at the same time.

It's best to consult some pros who can look at your overall financial picture and advise you on the optimal structure.

Am I optimizing for full time in my business?

It is likely you will be unable to find a property in the optimal location, I would not hesitate to consider investing in a property in close proximity but not directly near the medical school so you can get a property before you no longer have verified income for a traditional loan. 

That's why, most of the time, you can optimize your project's IRR by selling earlier than what you would expect because you can properly time your big pay-off date (i.e. your property sale date).

I'm a #s guy too, so I definitely understand where you're coming from, but there's also a point where it's more beneficial to just get started with a decent property, than to run more analyses trying to find the "best" or "most optimal" property.