There are plenty of sites relatively close to shore. You can see the stand pipes from shore in Port Aransas and I've made good boat dives on the north jetty. The distance is more often a function of where the blue water line is located. People generally go farther offshore to get clear water. I've seen clear water all the way to shore in Corpus Christi. It's rare, but it happens. 20-30 miles out during the summer will usually do. A 25' boat will generally do, but not as many days a year as a 30' boat. I wouldn't get too hung up on length. Arguably more important are features such as a deep v, self bailing cock pit, good radio, 2 motors, etc. Don't forget the stern/transom. Taking a wave from behind can get you in a hurry.
Sorry to be so general, but yours is a difficult question to answer given the highly variable conditions in the gulf and the subjective nature of what is "acceptable" in terms of boats and dive sites.
MG