DX will be fine, and cheaper, FX will also work, but will cover a fullframe if you ever chose to invest in one>- Street photography
24mm, will be roughly a 35mm on your body, though some may like it a little wider.>- Portraits
50-85mm will work, depending on you preferred working distance. You could even use a 35mm and it would look fine, and be a little more versatile. I would shoot for f2 or faster, on any length for this use.>- Landscapes
entirely depends on what you're shooting, a good sharp zoom with little distortion would be good I think.>- Micro photography (flowers, bugs, etc)
people seem to like the Tamron/Tokina 90mm Macro's. Could double as a longer portrait lens.
You could probably get by with a 17-50 2.8 for most of this. Wouldn't be super inconspicuous for street, but neither is a D3400 necessarily.
I would look at the focal lengths you use the most for different scenarios, and then buy a lens that improves upon that length. Also keep in mind that with your 1.5x crop sensor, lenses will be a little "longer" than what their focal length says (a 24mm giving the field of view of around 35mm). All of the focal lengths I listed are the actual focal lengths, not the equivalent field of view after crop. One last thing to consider is that the D3xxx line does not have a built in AF motor, so be sure that lenses you purchase have them inside.