Like others have said, if you are careful about what and where mods are definitely safe. I have 50-some mods in my game. I'm still running my years-old original save file with no issues and have never gotten a virus either. (Knock on wood! lol) I just make sure to check for updates before loading up my game.
Those updates are the biggest "problem" I have with mods, but what they add to my game makes it completely worth it. My advice is to bookmark the individual mod pages so you can get right back to each of them to check for updates.
I would try dipping your toe in with a small mod that adds a feature you want or fixes something that annoys you. I'd suggest UI Cheats as a first step. While I agree with others that MC Command Center (MCCC) is a must-have mod, it can definitely be a lot for a first time mod user to handle.