Background: I have an MPH which I did mid-career. I learned a lot and am in a job where I use some of what I learned in my MPH every day. I get to do interesting and important work. I make a good income. I am not against the degree at all.
That all said. I wouldn’t recommend going right out of your BA/BS if it means going into substantive debt (which you would be). You won’t get a much of a salary boost over someone with only BA/BS when your graduate. You will still be considered entry-level for the most part. IMO an MPH (like an MBA) is a degree where will get more value from the schoolwork if you have some real-world experience going in to the classes (even more so for an MBA, but I think true for both). An exception would be if you wanted to do lots of epi and biostats. Then the degree may set you up for different roles, even w/o a lot of experience.
There are a number of MPH programs that are part-time and programs meant for working adults, which will save you $ since you aren’t forgoing a year or two of income…your employer may even pay a hunk of it (mine did).