Camera screen/LCD is small and brighter, when view in PC Monitor, depending what monitor, the brightness will be less 'oomph'. Something like you view photo in your phone, you adjust the brightness to max and low. On LCD/LED, viewing angles can affect too.

By default, there's already picture styles.
In your camera, by default it may apply "Standard" picture styles.
When you import into lightroom, it will apply Adobe's standard color profiles (or picture styles).
You can change it to "Camera Standard" to match your Camera's color profile (or picture styles), but may not be 100% match unless you're using Nikon's ViewNX or CaptureNX.

You mentioned you like wide angles, FX have better ultra wide angle lens option. There is wide-angles for DX, but if you really prefer ulta-wide angle shots, FX have better available option/choice. If you invest on expensive DX lens, and later you plan to upgrade to FX, your expensive DX lens resale value is... kind of low...

If you'll be using for long-term the FX will be a better investment, and also better resale value which is also due to DX line being replace more frequently.
Not sure about entry level FX like D6XX though, it's sort of a new line.
DX series D7XXX replacement is about 2 years.

Anyway, just sharing my "personal" opinion, since it's also for company and there is budget for it.

When shot in CROP mode (DX), the resulting RAW file will be around 16MP and smaller in size?

Usually LCD/LED Monitors is more bright/cool.
When the photos are printed, it will differ a lot from those uncalibrated LCD/LED monitors in terms of brightness and temperature.

And Mobile Phones, usually the photos will look nice, vibrant, punchy, sharp.

Not just laptops, even those office used LED/LCD Monitors, they're cool and bright.
Usually after adjusted, can see the huge difference especially the before and after.

HDR like - Depends. Some people may like it, but it looks too unnatural. Some people may look at it as "unique", but it's a different feel. For me, can provide original natural version, then HDR version, B&W version, or other "effect" version. The original natural is still the most important. For effect, the customer can add their own filter/effect using software. But those with "effects" applied, it's a different story.

Just my 2 cents.

Btw, seems like the photos has green tint? It look greenish, but some people may like the tone tough.

Make sure the focus is correct. At widest aperture, the DOF can be very shallow especially if you're at closer focusing distance.
Even when your focus is lock-on, your focus may run if you "moved" or there is back-focus/front-focus issue.
To test, out your camera on tripod and capture. You can compare with Live View Focus result to confirm any back/front focus issue, and don't shoot too close to your subject.