Recommend a directory plug-in?

I hope this is okay to post. I’ve been looking around for a good business directory plug in and although I have found lots I thought it would be helpful to get some impartial feedback from people who have actually used them rather than just basing my decision on the sales pitch!

I currently have a directory on my website but it’s just listings, built in html and I’d like to move everything over to a wordpress installation instead. You can see what I currently have here: http://www.essexmums.org/directory.html

I would like to keep some features of what I already have and add some but basically I would need it to include the following:
* space for description, image etc
* address, with ability to search for a type of business by postcode, address etc (possibly with a map that locations are marked on)
* space for social media links
* ability to browse categories as well as search by location
* ability to have featured listings that appear at the top of the category pages
* users can claim listings and edit them
* users can pay for featured listings

Can anyone recommend a plugin to me? Thank you!