You can try SMF
simplemachines.org, it's really good I think, forum package is a successor to the php version of YABB and is feature rich. It stands somewhere between phpBB 2 and vBulletin in the number of features it contains. They have a good reputation for updating security releases.
Benefits: It uses AJAX for some elements to make page loading faster. It has attachments and sub-forums. It features a package manager to install mods easily. SMF includes a file that contains functions which allows outside programs to interface with the SMF forum libraries, making it easier to integrate the forum with a website. The staff is helpful at simplemachines.org. It plugs into Joomla well with some modifications. (Update: as of the moment, the Joomla bridge is not available due to legal issues).
Drawbacks: It is missing some key features even compared to phpBB, such as e-mail through the forum and group moderators. Not as many mods as the other forum packages. It has the fewest community based mods (i.e. profile enhancements) and the fewest overall mods compared to phpBB and vBulletin.
[AD]Conclusion: SMF is probably the most full-featured of any free forum package. The latest version had a shortage of good templates for a while, but that is quickly changing. The SMF package manager is one of it's best features as it allows users to easily install most mods with just a few clicks in most cases. Note that for non-default templates, you may be required to manually add some code since most mods are written only for the default template. The big drawback of SMF is that it has fewer mods than phpBB or vBulletin.
Any basic plan with mysql will let you to download and install smf, look into hostww.net, inmotionhosting.com or mmhosting.com shared hosting deals.