Congrats for rescuing a dog from the shelter! He will be very aware you have rescued him and will be very appreciative for the rest of his life. Unfortunately, like most purebred dogs, English Bulldogs have a lot of health issues, but unless you're not financially able to take on a high maintenance dog, I see this as no reason not to rescue the little guy, as it's not his fault he was inbred. In fact, sometimes helping a dog through these problems just makes you closer.
This breed has a lot of eye and sinus problems. They tend to develop infections along their eyelids which can have a discharge. You just have to keep an eye on it (pardon the pun) and make sure it doesn't get infected. They can easily get Demodectic Mange and other skin problems. If he's solid white, he may have even more skin problems. They are also prone to pretty bad allergies, thyroid issues, heart murmurs and hip problems. And if you live in a warm climate, NEVER leave him outside on a hot day or leave him in the car, as they are extremely prone to heat stroke. If you're looking for a dog to go running with you, this is not the dog! They do not tolerate much exercise. They drink lots of water, so make sure he always has plenty available. Basically, they look like tanks but in reality they are very fragile dogs. That being said, they are normally very loyal and can be very affectionate.