How Do I Secure a Server

My brother has a server on which he runs several websites and told me that if I can demonstrate to him that it won't pose a security risk, we can talk about him hosting a server for me. I've only ever hosted LAN before, and know next to nothing about network security.
He wants to know:
Will it be publicly accessible? If not, how will you give people access?
I plan to put up a whitelist and only give the connection info to people I know and trust, but I'm not sure that's what he's asking.
Will it make the servers a target for any kind of denial of service attack or retaliation?

Would anyone be able to help me answer these questions, or point me to somewhere I could find information to learn more?

Thanks
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