Most lawyers who offer advice on a question like this will ask a lot of questions to dig deeper into the details before offering advice. I have about fifteen that I go through when somebody is asking for advice on whether to form a nonprofit.
First, some background to be sure we are on the same page. There is a difference between being a "nonprofit corporation" (which basically means that income received by an organization does not get passed along to any individual owner) and being "tax-exempt" (which means that the IRS will not expect the corporation to pay income tax on its profits.) When we talk about subsections of 501(c), we are talking about federal tax exemption. (Texas's corporate income tax is low, so the federal exemption is the one that you probably care about.) You can form a "nonprofit corporation" in Texas without receiving IRS tax exemption under section 501(c).
Without more information, a fan club is not an easy match to fit into 501(c). From what you have described, you're pretty clearly not creating a 501(c)(8) or 501(c)(10). It might be a stretch to fit into being a "charity" under section 501(c)(3). A 501(c)(3) must be "organized and operated exclusively for religious, charitable, scientific, testing for public safety, literary, or educational purposes, or to foster national or international amateur sports competition ... or for the prevention of cruelty to children or animals." But it's not unprecedented. For example, the "International Jack Benny Fan Club" has maintained 501(c)(3) "public charity" status for decades. And there is an "Tupelo Elvis Presley Fan Club" that is exempt under 501(c)(4). And, if you set up a membership system, exemption under 501(c)(7) as a social club is a possibility. There's at least one 501(c)(7) that is devoted to bringing together fans of "Disneyana" memorabilia.
But back to the questions at the top. It's not obvious to me that forming a nonprofit, or pursuing tax exemption, is a perfect match for starting a fan group website or club. There are costs associated with doing that. There are compliance issues, like making sure that the nonprofit's money does not flow to the private benefit of you or other conflicted people or avoiding "self dealing." If you think that the tax benefits of nonprofit status overcome those costs, schedule a talk with a nonprofit lawyer.