At the consumer level, there's not a lot you can do.
This is the equivalent of you being inside your house, and an incessant mob outside, continuously knocking on the door. So many of them, it blocks your pizza delivery.
Pretty much all you can do is lay low for a day or two until they go away.
Ive blocked them on skype. I went offline everywere they can contact me. It has been about 20 minutes since this happened and I bet they forgot my ip. Anyways, they were 12 year olds and 15 year olds. Dunno why it freaked me out.
I seriously doubt that the childishly behaving individuals that you kicked from your server have managed to develop a hack to enslave large numbers of computers (a botnet) necessary to effectively attack your I.P. address. Should they choose to utilize their own equipment, from their own I.P.'s, that would seriously cut into their gaming time, and readily identify them to your, as well as their own Internet Service Providers. Although it would be monumentally dumb for them to do that (although I think you have already established the fact they aren't the brightest bulbs in the drawer) people who are actually going to commit an illegal act don't usually announce it in advance.
When you are admining your server, make sure that you have set out clear, specific, policies (rules) that everyone is expected to follow. And broadcast them to all players. That way when someone breaks those rules, everyone on the server knows exactly what to expect (they're going to get kicked or banned).
F*** 'em. They probably won't do anything and even if they wanted to they probably don't have the resources.
But for the sake of the question, you should start at the router.
Close all unused ports, use shields up! https://www.grc.com/shieldsup to check and see what other people can see from your connection.
Some routers have a DDOS prevention/mitigation option, turn that on obviously.
Turn off "respond to WAN ping"
A DDoS attack attempts to push you off the internet by literally flooding you with data. A more powerful system can cope with the load better.
Now, I doubt this will happen, but if you do come under a serious DDoS attack, start logging the requests coming in. If it goes on for long enough you can get your ISP involved and have them ban certain IP ranges.
TL;DR Batten down the hatches and keep your helmet on, you'll be fine.