What documents do they require, what credit scores do they allow, how do they verify previous rental history, etc.?

I'm currently in Potomac, working at a private school here. 

And are you targeting a certain zip code in LR or a certain neighborhood/area/school district?

Quote from @Gregory Wilson: A few things there, Brendan.First, an LLC with you as a member and your (wife, son, pal, etc.) partner as a 1% member will file a Form 1065 which is about one tenth as likely to be audited by the IRS as a Form 1040 with a Schedule E rental activity (which I presume you will attempt to show is an active business).Second, you want an LLC because when your local Alabama handyman drives his girlfriend's uninsured truck into a van load of U of A medical school interns on I-22 when he goes  to get some shingles for your roof, on your business, you don't lose everything you have or ever will have to an uninsured claim. 

I have some news for you, FHA does NOT require a 1 year work history!

The policy was $2200/year ($1.1M Bldg coverage and $1M Business liability coverage in this apartment LLC) and I haven't had a single claim in my past 5 year history.

Samford's business school also offers a concentration in real estate investment and management.

You might get lucky and get matched right away but chances are, there isn't a fire happening right were you are at, and with the right home / school / budget, etc. 

Our home is located in a great neighborhood, right next to excellent schools, close to several hospitals, and other amenities. 

Verifying last 2 years of rental history very important!