In the event that you and your girlfriend break up during residency or after it will be far more complicated to co-own it.Imo your best option is to rent as cheap an apartment as possible in residency and reevaluate your situation once you have an attending position.

I also figure repairs to bigger assets would be much more complicated such as the mechanicals.

Do you see any complications with obtaining financing from a future re-finance or from purchasing future property where I can use the free and clear home as collateral?

Of course, if it turns out it's a great  rental and you don't need the cash, just hold it as a rental even longer, skip the 121 exemption and use the 1031 whenever you're ready to sell.If it sounds complicated, it sort of is, and you must have a Qualified Intermediary on your team prior to selling your property in order for the 1031 to be valid, so the first step would be finding a trustworthy CPA and QI to make sure all your tax docs are in order.

Unfortunately too complicated to put in a post. 

It's not really that complicated to buy out of state.

For the Average buyer this would have been disaster.. we simply built a new construction on it and did OK.. but this full blown rehab can be a real challenge for many .. its one thing to replace kitchen baths paint carpet roof.but when it comes to structural or these really old houses you get from Charleston north into New England.. etc its far more complicated and risky.

But your situation seems more complicated, so I advise you to watch bp-podcast-109/ and talk with @Scott Smith.

This would be my first deal so I do not want too many complications.

Like @Frank Chin said it can get complicated over the years.