Well I normally don't keep my machine on 24 * 7. It uses more power then what is worth it.
I wouldn't advice to run public server from your local PC. Well yeah you could but you need good network peering + connection. Question is are you using this server for your learning and testing purpose or for your clan. If later is the case then rent the server from professional hosting services.
If your router supports you can use dynamic DNS. So whenever your IP changes it gets updated by itself.
