I'm looking for some suggestions.

Marathon perhaps. Made for the military. Good mixture of mechanical and quartz pieces. General Purpose line has a few options that fall into your desired size range. Fairly monochrome across the board, so fits the requirements around colors. Have a look.

Bertucci and good ole fashioned Seiko 5's might also be options.

For basic I would go with a gshock or the lauded f91w. Both are tough, light, and have alarm and stopwatch functions at the very least which can come in handy surviving basic. After that it really depends on her MOS on what would be appropriate. Infantry? Probably still the Gshock or if she prefers analog like I do then probably the marathon midsized diver (the small one) with a black dial. The case itself doesn't need to be black necessarily but it shouldn't be reflective or polished either. Maintenance or motor pool? Probably something similar. Intel? Something nice, respectable, and robust enough to use if needed, but that looks smart on her as well as she may be briefing colonels and generals one day. Most importantly DO NOT get a Bluetooth watch as there are some classified environments that it would not be allowed. Finance or any other rear echelon/support position? Whatever makes her happy generally speaking. 

Tbh if she has a Gshock, f91w, timex expedition, etc to wear when she needs a true beater then it doesn't really matter what she wears the other 85% of the time.

Most young enlisted Soldiers don’t wear nice watches. G-shock would make sense. Fitness trackers are also common. Army guidelines are not very specific but state something to the effect that watches should be conservative. Staying with black is a great idea. G-shock could be worn in the field and at boot camp, but once she arrives to her first duty station after training is over, she can wear something nicer if it makes sense for her MOS.

G-Shock, Marathon or even Bertucci. Depending on whether or not you want to get her a quartz or mechanical? I could see the G-Shock being more robust and not having to set the time like a mechanical would be a bonus for her. Even the new bluetooth versions that sink with your phone would serve her well.

Good luck in you're search 🙏

G shock, marathon, Victorinox, or if you don't mind spending a bit more perhaps a CWC quartz?

What about the Citizen BM8240-03E? Just for telling the time, day + date. This is 36mm - if you want a chronograph function, you'll struggle to find anything below 38mm case.

Thanks for the ideas, I think I found a Victorinox that she will like.  I didn't even think to look at their stuff.

This is what I found for her.  I have also ordered a couple differen nato straps.  Those are very hard to find for such narrow lugs.