How would I advertise my server?

Just post it on all the mc listing sites, make YouTube videos, invest in cheap ads from Google etc

MCServers.Org
Minepick.com (I think it's .com)
MCServerList.net
minecraftservers.net
theminelist.com

best way to get your name out is make a server listing on here and set up votifier that way if people like your server they can vote and your server can become one on the top list, then id recommend making a forum post in the server section, then go try out a few sites like minecraft forums. you can also make a free website at enjin.com which lists your server and they have a nice plugin thats easy to use that links your server to the website and displays info like whos online.

I'm a web designer. A website would promote a server? Please PM me if you're interested.

You can use many voting servers to get your server out there, such as minecraftservers.net/.org, and also use this website. You can write a thread post and make a server thingy in the server section of PMC.

EDIT:
You can also use the PMC Chat, the advertising section, but make sure not to spam. From there you can send a brief description + a link to a longer post (the forum post)