Join a gun club. You can rest assured that most gun clubs check their perspective members out fairly well. And since all the members are gun owners, you can assume that no ones is going to come in to just commit suicide on the range. They can do that at home. I went shooting just yesterday and for a large portion of the time, it was just me and my two friends there. Much better than a public range.
Good suggestion about a club. I get creeped out when you sometimes have 1911 cowboy guys/Clint Wannabes who are not as careful as they should be. Gun safety is the most important thing.