I would recommend a free forum software like Forumotion and eventually pay for it unless you're really serious about this. If so, then I would definitely use XenForo (the software this forum is hosted on). It's the most efficient paid forum hosting software since you don't have to use any plugins like you do on VBulletin.
I would strongly suggest, as @Yoshioka Seijuro and @Beerus mentioned you start out with a free solution. If you want to start with a hosted solution, that's completely free to utilize, something like Forumotion or Proboards would suit your needs. If you want to host it yourself on a .com or other tld, then you'll want a solution like SMF, MyBB, Flarum or something similar. I would not start out with XenForo, IPS or vBulletin right out of the box, as these are quite expensive and if you are unsure what you're looking to do with a forum, it wouldn't make sense to spend that sort of money on a tinkering project. Start small, build up, then upgrade to the "good stuff."