You've gotten some great information from Deja. Unfortunately, there's really no way around the horrific commute, especially to and from Medical Center at rush hours. If you're fortunate enough to be working at non-traditional times, you'd be 10-15 minutes away from pretty much anywhere.
Some questions ...
Are you looking to lease or purchase? For the moment, I'll assume the former.
What is your budget?
Preference as to single-family home, townhouse, condo, apartment complex, etc..
How many bedrooms/bathrooms ... some 1 br. units can be really small.
Are there any pets? Do you smoke?
Are there any credit or previous landlord/tenant issues?
Will you have sufficient cash for both the security deposit and first month's rent?
In any situation, you'll need to be prepared to act quickly, as the good rental units are gone almost as soon as they become available. I'd begin the search in earnest about 45 days prior to your move.
Please note that there is no cost to you as either a buyer or tenant, so working with a Realtor, especially one such as myself (my wife/working partner and I have welcomed dozens of new Houstonians over the years) is pretty much a no-brainer.
If I can answer any additional questions, please feel free to get in touch.