I just want to say that you're probably worrying too much about it. Of course, there is lots of things one can do to improve security (which the others here are listing dutifully) and it is foolish to just assume that one's computer is entirely secure, because as a user, you will always have the ability to bypass that.

But there's a pretty firm consensus in the IT industry that Linux is more secure than Windows. And that the popular Linux distributions are more trustworthy organizations than Microsoft.

So, it's good to inform yourself, but if you survived on Windows, you at least should not worry about the Linux side of things. It's more than fine.