My turn . . .
Nikon. If you can afford the later 5xxx camera like the D5600, I would get that rather than the older D5100.
As
@Strodav said, IF you can afford a D7200, that would be a good option.
KEH is a good source of used gear. They used to have a holiday discount. I am hoping that it will be on 'black Friday," as I want to pick up a D5600 for my school.
I agree with
@Strodav on the 18-140. I have that lens and it is a GREAT general purpose lens, and often the only lens that I need.
The only additional lens I suggest, would be the 35/1.8 for LOW light indoor photography.
And you have a nice 2-lens kit.
As for the 70-300, do you NEED the reach of a 300?
That would depend on WHAT you shoot.
Caution, all Nikon F lenses are NOT compatible with all cameras. You have to look at the compatibility table.
The D3xxx and D5xxx cameras do NOT have an autofocus motor in the body. So for autofocus, you need to get an AF-S or AF-P lens. NOT the AF or AF-D lens, which require the AF motor in the camera.
Caution: The AF-P lenses will NOT work on older cameras. It may not work on a D5100.
The D7200 has an AF motor in the camera, so it will autofocus the AF and AF-D lenses.