The most critical thing as a SQL Server DBA is to ensure that your databases can be restored in the event of the loss of a server for whatever reason: disk crash, fire in the server room, tribble invasion, whatever. To do this, not only do you have to back up your databases, you also have to test restores! Create a database and restore the backups of your production DB to them. It’s the safest way to make sure that everything works. This test restore can be automated to run every night, but that’s outside the scope of what I want to talk about right now.
There are lots of places that problems can creep in, this is just one part of how you’ll need to monitor systems. This is how I’ve done things for a number of years, and thus far it has served me well.
Depending upon your instance count, average database size, maintenance windows, etc. etc. etc., some of these things may or may not work, but the principle is the same: protect the data, and automate your processes to protect that data. This is a good article to read for ideas, and then from there dig into other administrative blog posts, videos, and books to become better versed in the tools and techniques available to protect your data.