I use SSH a lot, and I mean, A LOT! Because I manage 3 other servers, and they are located in different parts of the world, I rely completely on SSH to keep them up and running optimally.
One effective method to mitigate brute-force attacks and attempts to break into your public server via the SSH daemon is to use the appropriate iptables rule that will handle such abuse. There are a couple that do the job really well but the one I personally use is one that works on both, dedicated and virtual, servers.
Every time I set up a server, the very next thing I do is secure the Secure SHell Daemon (sshd).
My checklist for doing that looks something like this: