I used Nikon DSLRs for many years and can confirm that they are very nice 'photographers' cameras. There is no significant difference in image quality between the 'entry-level' models and the more advanced models. Entry-level models tend to rely more on menus for making adjustments, while more 'advanced' models have more knobs and buttons, which make changing settings quicker, if you know what to do with them all! The entry level models usually have good-quality plastic bodies (which are lighter), while metal bodies, with weather-sealing gaskets, are used in more professional models that are expected to receive hard use.
Having said that, it is the lens which actually makes the image, so do not skimp on quality here. It is also the lens that will contribute most of the weight, especially if you are a wildlife photographer, with a need for 'long' lenses. The D3400 uses an APS-size sensor, which is smaller than the 'full frame' sensor(i.e. same size as 35mm film), used in larger models. The advantage for the wildlife photography is that the smaller frame provides more 'telephoto' effect from any given focal length. In this respect, a 105mm lens on an APS sensor has a similar effect to a 160mm on a full frame camera. (I've written a
comparison of different sensor sizes on my website, which may be of interest)
With my own Nikon cameras, I used a Tamron 90mm macro (which was a highly regarded lens at that time) and often added a 1.4X teleconverter, to give a little more 'reach'. This worked well for me, over many years but, as I got older, it seemed to get harder to approach an active subject like a butterfly, without disturbing it, and my knees objected to the low viewpoints that were often needed.
A few years ago, I changed to an Olympus 'mirrorless' camera and like it very much. Not only is the camera body very light but the lenses are smaller and lighter as well, while the overall system still provides image quality equivalent to the best APS-size sensors. Mirrorless bodies are becoming increasingly popular with Fuji, Sony, Olympus, and Panasonic, all providing good examples. Canon are rumoured to have a new mirrorless body in preparation and Nikon are sure to follow suit. I was won over after I tried an Olympus in my local John Lewis store. If you haven't experienced one, it might be worth at least having a look, to see how you like the style.
I'm sure that, whatever you choose, you will like the quicker and more direct operation, when compared with the 'Bridge' style.
Mike