If you want it on 24/7 you'll need to run it from a dedicated server. Dedicated servers will increase the speeds of your server exponentially, but they're expensive. I currently run all of my own minecraft servers from a dedicated, I'll be offering this to users soon =D
Expensive? They actually cost money? Well, then nevermind.
I'll just have to live with running it myself.
A dedicated server is a computer that sits in a datacentre. The function of a dedicated server is to run things that need to be online 24/7, for example minecraft.net is run from a dedicated server, this place is run from a dedicated server. Dedicated servers, depending on the specification cost anywhere from $50/month to $10,000/month. I'm in the process of building a site where users can register for a minecraft server and have one hosted from one of my dedicated servers and they will be online 24/7, however it's still being made.