For some video training, you can look on youtube for Graham Houghton and FZ200. He has lots of tutorials.

At Long zooms steadiness does help.

Not something "wrong", but different compromises to make the camera possible.
Those long zoom lenses would not be possible at a reasonable weight and size on a 35mm frame.

The fz200 compromised on zoom to maintain aperture at 600mm.
The sx50 compromised on viewfinder to maintain a size and price.

Have to decide which compromises make a better camera for YOU, and HUBBY!

It has auto focus and manual focus options on the side of the lens. Manual focus is pushbutton so its indirect. F2.8 at 600mm zoom is pretty good. It is a 1/2.3 sensor though, so you've probably taken it off the list.

The fz200 hit a price of 300 during black Friday and cyber Monday sales.
It is a nice camera with a constant f2.8 aperture throughout the zoom range. none of the other long zooms have that.
The sx50 has been replaced by the sx60. In some respects the sx60 is not deemed as good as the sx50, but it may just be the high bar of comparison.

The 18-140 is my favorite of the 18-x group. You already have the 70-300 which is next.

Can you get the dx 35mm prime?

Sx50, fz200, and P520 are all very good choices with differences in the details
Hot shoe: sx50 and fz200
Raw : same
Lens : shorter range but brighter on fz200
Resolution: p520

See if any of those make a difference to your needs

Why isn't anyone suggesting the successor models?
P520 - p530 or p600 from nikon
Sx50 - sx60 from canon?

Not just budget reasons, although I know that's a consideration.

For my d7100 I have the 18-140, 70-300, and 35mm DX prime.
The 18-140 is the second newest 18-xxx lens and was designed after the 24mp sensors came out.
The newer 18-300 is slower at 300 than the older one.
The 70-300 is probably the best value for money in the zoom lenses. Better auto focus than the 55-300.

And then the 35mm is the low light portrait lens.

See if you can still take advantage of the lens bundling deals.

Sadly, gps on cameras is not as useful as it could be.
My A65 takes so long to figure out where it is that I don't bother with it.
The D5300 that the op has should be better, if my nikon's with gps are similar.
But gps barely works indoors, so once you are in the museum, at best it will use the last location.
Having a logging app on your phone should help, but it is an extra step in the workflow to match up the log with the pictures.

So I would use the gps in the camera, and have an alternative also.
Pen and paper, spouse, cell phone establishing shots, cell phone log, take a quick video,

Lots of good suggestions in this thread.

Thank you for the suggestion, I saw the spring, and haven't had any opportunity for careful trimming.

Learned something about the sx60 the other day, with a cover over the hot shoe, it won't let you control the internal flash.

Agree that it's hard to focus at times.

Wonderful all the responses to this question that represent individual understanding of the answer to the question. Hopefully one will help the OP get out and take pictures.

This question is one of the most confusing things about digital cameras.

What does crop factor mean?

My own understanding is:
The crop factor shows what the equivalent field of view is relative to a standard.

The standard is the classic 35mm film camera, that we all used to love.

So, in Nikon terms:
FX = crop factor 1.0
DX = crop factor 1.5
CX = crop factor 2.7
And for compacts
1/2.3 inch = crop factor 5.7

Without doing the math exactly, the captured picture on each of the sensor above would be about the same if you take the value FX / crop factor.

50mm FX / DX crop factor 1.5 = 35mm
50mm FX / CX crop factor 2.7 = 18.5mm
50mm FX / compact factor 5.6 = 8.9 mm
All of these will yield just about the same picture, with a little edge variance, since the math was not exact.

That's why Nikon created the DX 35mm f1.8 and the 18.5mm CX f1.8

FX cameras can detect a DX lens, and reduce the size of the image they capture to match the image circle needed for a DX sensor. You can also turn that feature off, if the vignetting is acceptable to you. The 35mm DX lens is usable for me on an FX camera in FX image size.
There are other considerations such as depth of field for each sensor size that will affect the look of the picture, but what is captured will be about the same.

Going the other way, to find the effective field of view on the smaller sensor, you multiply.

FX 300mm x DX crop 1.5 = 450mm
FX 300MM x CX crop 2.7 = 810mm
FX 300mm x compact 5.7 = 1710 mm

That is the "reach" advantage of smaller sensor.

All this doesn't really matter, get out and take pictures, and see what you see through the viewfinder.

Of course, this question will be beaten to death as each new photographer comes to his or her own understanding of how to get the shot..

Nikon lenses are generally compatible with most cameras. DX format lenses will mount on FX bodies, with no issues. Some even perform with an acceptable level of vignetting. The DX 35mm prime f1.8 is fine for me on a D600 in FX mode. The DX 10-24 is also said to be ok above about 16mm. Haven't tried that one out, though.

Your friend is correct. The Field of view equivalent of the 17-55mm DX lens relative to an FX lens is 25.5mm-82.5mm lens.

Crop factor is a confusing subject.

Look for the "Lens Simulator" on the Nikon.com website. It can help you visualize the effect.

The 14-140 would be better for indoor shots because of the wide angle. It is relatively slow, based on the aperture range.