Why bigger than 9mm? It's so widely used for a reason, better capacity and more controllable particularly out of the lightweight compact pistols that are comfortable to carry on a daily basis. I've seen you ask a lot of questions about the G3C, for your price range that's pretty much your main option. They also make them in .40 S&W for another caliber option.

If you're looking for a conceal carry that's compact in .45 ACP (if that's what you mean by bigger, "Larger Caliber"?")
They're many to choose from here. I personally would suggest finding a range by you that rents guns so you can see what you're comfortable with in that price range. Otherwise, you're just gonna have folks here give opinions. In the end, You have to be comfortable with the pistols grip & overall feel.