You can use WordPress plugins to create your own web directory. There are premium plugins and themes, or you can try the free plugins. Expect to do some work, making some changes to HTML and CSS code and work with an FTP program. If you can’t (or won’t) do the extra work then look at the premium options instead. However, if your plan is to make money with a web directory aren’t you smarter to use free options and do some of the work yourself? Note: I do pay for software and themes and even the odd plugin, but I prefer to give business to the open source and free software as often as I can.
Link Library is the plugin I have been using longest. You can work with the links you already have in your WordPress blogroll. Take a look at the information given for setting it up. It is fairly simple and most of the work is just done inside WordPress itself. Pretty simple.
Open Links Directory is the one I’m looking at and thinking I will start with for a new directory I’ve been wanting to sort out and get active. See the demo. I’ve done the install but I’ve got a bug to work out with FTP. Your own install may be bug-free. Other than a small bug, it looks great and I’m impressed.
WP Link Dir looks interesting and they say it works with pages on WordPress instead of posts. So that could leave you with the ability to run posts as a regular blog with the directory in the background, or as a feature. I’m only hesitant to download this one because they want to gather your email address first. (I don’t like having my email address harvested for spammers).
Outdated, possibly forgotten plugins which you can still find to give a try:
Web Directory WordPress plugin has not been updated for years so it is use at your own risk. But, you can find more information for using and installing it on the site (the download link there is broken).