My recommendation would be for the combination noted below. For this you get Nikon’s base DSLR and two very good lenses. Do not be fooled by it being a base model, it is a fantastic bargain. It produces images near indistinguishable from Nikon’s more expensive models and its a great starter camera (I have the previous model D3300 and the top of the range DX body, the D500. Sure the D500 is a better camera -it should be, it’s 5x the price. But image wise nothing much in it.) OK it not as robust as the higher cameras, but a youth dropping a camera is going to break either and it’s less painful breaking a cheap one. Oh, and that kit and camera is light and suitable for smaller hands too.
Do make sure you get (as noted below) the AF-P and VR versions of those lenses. VR gives you useful image stabilisation (Vibration Reduction) and the AF-P lenses have turned out to be great and fast focussing lenses. If you can get as a kit as Nikon have been doing then great. It is even worth putting that together if you have to buy the 70-300 as an add on. That lot should allow you a bit over to buy some SD cards and a spare battery and maybe a cheap camera bag to keep it in. Finally, consider a tripod if there is anything left over. Very useful for video.

Nikon D3400 DSLR Digital Camera + AF-P 18-55mm VR + AF-P 70-300mm VR

As an owner of a DSLR kit, I will say that one of the factors you are forgetting about is they are heavy and unwieldy items to carry all day unless you spend more $$$ on a carry system.

I would recommend having a look at mirror less cameras instead.
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This. Also, the added mechanical complexity that a dslr brings with it more or less goes against the required ruggedness. Mirrorless systems are pretty good nowadays!