Yes it is possible. I have ATT U-verse myself and have hosted web sites from time to time. The biggest issue you will have is that if you do not have a static IP we will have to use a dynamic dns provider which if you want to use your own domain name would have an additional cost.
Also, you would need to have access to your router so we could open up the necessary TCP port to allow the traffic in.
What sort of server / OS are you considering? I am proficient in both Linux and Windows web hosting so which ever way we go I would have you covered.
Look forward to working with you.