I've once wanted to make my own server to host games for me and some buddies. But, honestly, I could say that from what I've been through you're better off buying a dedicated server. Having a server machine to yourself is not only expensive, but you're limited to the internet up/down speeds that you get from your internet provider. Also, if you had your own machine, you would access the server files directly, not via FTP, unless you went through the process of also running your own FTP server, which in my opinion is too much work for a server on this scale in this case.
There are dedicated Minecraft server hosts that provide you with FTP access, creating a website along with it and more importantly much cheaper than building your own server. I've bought dedicated servers before for about $20 a month and had no issues. Speeds are great, as long as you go with a server realtively close to your location (mine was ~300 km and my speeds were still good).
I'm not familiar specifically with Minecraft server providers, but I know that you can find what you're looking for, including FTP access and web domains. Personally, I think that if you're running a server for just 10 people, don't even pay extra for a website. Start off with something simple like a Facebook page or Twitter account if you really want to.
I know some people who have had good experience with Multiplay. They offer a wide variety of dedicated gameservers, including Minecraft.
