I have thousands of rounds downrange with M16 and AR 15's. I have never experienced a discharge that was unintended. I have seen it happen, but will say that each time it was with a AR that had been modified and tinkered with by someone who really didn't quite know what they were doing or why they were doing it. With a new as-manufactured rifle, please consider the advice previously provided and shoot it as is for a while prior to falling into the "I gotta modify" abyss. Honestly, most of the time it really doesn't need to be done.
The advice to spend money now on ammunition and magazines is very sound. Without those, the piece is a decoration only.
What make and model did you get?
The vast majority of them get the job done quite well without making any alterations. Now, if you get into target or competitive shooting, that would be a different story, and purchasing a higher end AR could be the solution.... but I don't know what you have now.
I recall an earlier post about getting one for your husband I think.