Custom forum

I am making a forum, and I'm okay with using a pre-existing forum software, such as Vbulletin, phpbb, etc. However I need various changes made to the software.

For example, with most forums, the homepage is a list of all the board titles such as (this is just an example site):
http://www.top-law-schools.com/forums/index.php

However on my homepage, I do not want this list. I want it to be a clean homepage with just an RSS feed, a log in area, and a search bar. The search must search only board titles (not text within threads, not thread titles, etc). Then someone can type in the board they want, and it will take them to the thread page.

For example, on that sample site, someone can type in "Law School Personal Statements" and it will take them here:
http://www.top-law-schools.com/forums/viewforum.php?f=18

Also, I want there to be some way of letting users add new boards. They can fill out some sort of form or something to add a new board, and submit it to me. I can then approve or reject submissions. If I approve it will become a new board, if I do not it will not.

Other than this, there are minor stylistic changes. The search bar has to remain at the top. The default headers, etc have to be changed around, some links should be deleted, just stylistic changes.

If you have further questions feel free to ask. I do not currently have a forum set up. I have a domain name but I do not have any forum software installed. I wanted to wait to discuss which software would be best for the type of site I am creating.