I would get the Nikon D3400 kit with ONLY the 18-55 VR lens, for $400.
IMHO, the long lens without VR is a waste of money. The longer the lens, the harder it is to keep steady and get a good picture. Save your money for a VR version of the 55-200 or 70-300 lens. I've used both VR and non-VR lenses, and I much prefer a VR lens for general use.
Canon probably has a similar entry level camera.
Another option is the Olympus OM-D E-M10-mk2. This is a mirrorless micro 4/3 camera. It is currently discounted because Olympus has released the mk3. You can get the E-M10-mk2 + 14-42EZ compact lens for $430 reconditioned from Olympus, or $500 new.
If you don't mind buying used, you can get some great deals, and your $ will go farther. But just like buying a used car, you have to be careful. Most of my camera/lens gear is used, and I have been happy with them.
If you buy from
KEH, they will warrant what they sell, vs. zero warranty from an
eBay seller. Manufacturer refurbished is another good source of gear with a warranty, though the warranty is shorter than for new gear.
WARNING1, if you buy a "gray market"/imported Nikon (did not get imported into the US by Nikon USA), Nikon USA will NOT service/repair the gear at all. This is why I will NOT buy a gray market Nikon. I want to be able to get my gear repaired, if it needs to be repaired.
WARNING2. For used gear, manufacturers warranty is generally to the ORIGINAL purchaser, and NOT transferable. And proof of sale/receipt may be required to obtain warranty service. Don't fall for someone saying you have X months of warranty left, cuz it drops to 0/ZERO when you buy it from him.