The simple answer is yes. However its not a license from BMI, ASCAP or SEASAC that you need. The actual establishment where the wedding/reception is held will be responsible for such performance licenses. You on the other hand will need a license from the record label for use of the master sound recording as well as a license from the publisher for each song. I don't mean to burst your bubble but in the context that you intend to use the music, you are not likely to be granted a license from either. It is likely considered a derivative work. You need to consult with an entertainment attorney specializing in music.
I agree with Mr. Parron that you will need separate permission to make and sell the copies of these songs you intend to put on your CD's. That will not be covered by blanket licenses provided by ASCAP, BMI or SESAC. However, if you do obtain the permission, which is akin to obtaining authorization for a music compilation (e.g. "Best of the 80's, etc.), you can obtain an ASCAP or BMI "website license" which will cover any use of the music on your own website for which you obtain the license. Save money by choosing one company or the other and just make sure that all the music you choose to feature on your website is appears in the catalog of the licensing company you choose. Most of my clients use BMI or ASCAP. I am not sure whether SESAC offers a website license. However I would be very surprised if they do not. All three have websites with very informative Q & A sections.
Legal decisions should not be made in a vacuum. There is no substitute for a traditional legal consultation with a qualified attorney with experience in the areas of law which are relevant to your specific situation. Please do not rely solely upon the answers you see on this website. They are limited by the small amount of information contained in the questions. These questions and answers do not create an attorney-client relationship.
For any given song you need one of the 3, not all 3. Look at their sites and catalogs of songs and chose the site that has what you want. By the way, if you happen to have $500M, SESAC is for sale. http://www.radio-info.com/news/sesac-back-on-the-auction-block-for-500-million
So far, this is free to you. Until you pay a fee, I am not your lawyer and you are not my client, so you take any free advice at your sole risk. I am licensed in IL, MO, TX and am a Reg. Pat. Atty. so advice in any other jurisdiction is general advice and should be confirmed with an attorney licensed in that jurisdiction.