Welcome to ask Ubuntu! Just as a comment, I think that your question is confusing. You might want to consider being a bit more specific as to what you want. I can't tell if you are asking if Ubuntu server is secure, or how it runs, or how to get a Minecraft server running, or what people recommend for such a server, or if any one knows of a guide,etc. You will get more answers to your questions if they are short and direct :)
Now I have no experience with servers, but I found what seems to look like a tutorial as to how to setup a Minecraft Server with Ubuntu. I'm sure you have the experience to understand it: https://github.com/endofzero/Minecraft-Sheller
I found this link in someone else question on Ask Ubuntu. Maybe you could try messaging those users about setting up a Minecraft Server, they seem very experienced: Interact with Minecraft Server
I see what you mean now :) I assume trying to setup a Ubuntu server for the first time will lead to some begginer mistakes. But that's how you learn, trying! Maybe start with the basics. Here is the official Ubuntu server guide https://help.ubuntu.com/12.04/serverguide/index.html It starts with the very basics, leading up to more advanced task. I suggest you setup a test server to toy around with, that way no damage can be caused. So make some coffee, sit back and enjoy a good read of the guide:p
Current Ubuntu images come with MD5 and SHA256 checksums. The checksum files are GPG signed with an Ubuntu public key. The public key is obtained verifiably from the Ubuntu keyserver. Easy-to-follow instructions are in How to verify your Ubuntu download.
To add to this, the binary images are signed by the Canonical Master CA, which has a chain of trust to a certificate in your machine's TPM, and will not run if tampered with and you run under SecureBoot.
Short of hopping on your bike and having the people at Ubuntu burn a fresh image while you watch them, I think this really is as good as it gets.
Best Answer
Windows has had a single-user ethos for a very long time. Even with the invention of NT and a role/privilege system, default installs would plonk users as king of the hill. Their account (and, more importantly, anything running as their account) could do anything to any file without a check.
This is huge because any application, any exploit in an application could run as Administrator.
It's only since Vista where that's trying to be reversed and tightened with things like UAC...
Source access is a double-edged sword. Open source enthusiasts usually tout security but it does also let people right into the system. They don't have to report anything they find, they could just write exploits for the hole.
Thankfully, most people do report any flaws they find. Even better is they sometimes include patches that can be immediately tested and distributed.
The turnaround for patching security holes does seem shorter than closed source software.
There are just fewer of us.
Sounds bleak but there are fewer people using one particular open source application. It's hard to justify writing an exploit, trojan, worm, etc when you could write one for Windows in the same time and catch a lot more people.
But we can't be complacent. There's no reason why a trojan or worm can't work in Linux. A malicious app running as a limited user can still do a whole load of damage. And the real flaw in all of this is the users.
Users are idiots who can be convinced to do almost anything if you dress it up with enough pomp or make it look like they're going to get something worthwhile from the process.
Read: Linux isn't invulnerable. Don't say it is. (Disclaimer: my post, my blog)