Now would be a good time to start looking for a Realtor. Believe it or not Realtors work with clients to find an apartment as well as single family housing.
Having someone to talk to during the process helps, if you are not familiar with Houston there will be many questions you will need answers to so hire a professional to make the process just that much easier.
Moving in May gives you a good time to find out more about the areas that you would potentially like to live in. Where will you be working and what is important to you to have where you will reside? Apartments generally have an idea a couple of months in advance since folks who move out are required to give notice. Pets, budget, commute, etc. will define what is best for you, so having an idea ahead of time will give you a leverage when you move here.
If you are interested in renting a home/townhome, it helps to look into that early on, as well. Generally these become available on the market a month or earlier before the lease expires.
If you have any other questions, please let me know.
Let us know if we can be of any further assistance! You'll love Houston!
The Loken Group
281- 861- 4624