Can very old, minor, criminal charges affect my being able to find a possition as a Rad Tech?

So I am going back to college to get an associates degree in Radiology to become a rad tech. My dad did it, and it worked for him. I am excited to do my classes, but I am also a bit worried that my criminal record might make finding a job difficult.

I have an assault charge, and a theft charge, both from when I was 19 years old (I'm 27 now and will be almost 30 when I graduate) and was a very different person in so many ways back then.

My dad who has been a rad tech for over 10 years tells me I ahould have no problem finding a job, but I doubt he knows the specifics of how the hiring process might be different for someone with any sort of criminal history, since he has none.

As long as I learn what I need to learn, do good in my classes and clinicals, this shouldn't matter much since its so old right? Or is that wishful thinking?

Any advice from anyone with any experience in the healthcare field who has old criminal charges would be greatly appreciated! Or if you know someone who has. Thanks!