The XQD format is a very fast one. When Lexar withdrew from the market, it left Sony as the only major player (with a couple of others make the format). But the Sony cards aren't cheap. If you only want to get one, I'd suggest 128 GB as the most practical size. And you can use a fast 64 (or 32) SD card as a back-up. I read somewhere that the new CF Express card will be slower than the XQD. (We're well invested in the card, since we have the Z7, D850, and the D500 -- all of which use it.) BTW, enjoy your new camera. You'll love it.
Mark, when I saw your question when I logged on this morning, I knew exactly what the issue was and I commend Bill for his quick inspired guess. I use a Z7 and also shoot in the "M" mode. I encountered the issue when I first got the camera last fall and it took me a lot of studying of the manual before I got the right setting for my needs (custom setting D8 to of "off"). But it turns out that had done nothing wrong. Nikon actually sets D8 (mirror settings in live view) to "on" by default and many people like it that way. Having the viewfinder/LCD displays mirror what you set is seen as an advantage by many shooters and by Nikon. So if you have set the shutter speed or f/stop wrong---or even white balance in Auto WB---you'll see that immediately reflected in what the screens show. Some people actually set their cameras according to what they see, that is, they change the settings until the picture "looks right." Many people see this as an advantage of using "live view." But there are many times where you don't want D8 set to "on." One is when you are using a flash in a less than bright indoor environment. In this case, you'll see a dark (or black) screen and viewfinder and basically have to guess where you're shooting! By turning D8 to "off," the camera sets the viewfinder/screen so that it is bright all the time, although it uses battery power faster than with the "off" setting. As for me personally, I like seeing the viewfinder bright at all times and I also use flash, so I simply turn D8 to "off" and leave it that way. The extra battery drain isn't that bad in my experience. As a general statement, the Z6 and the Z7 have some unfamiliar settings to those of us accustomed to DSLRs and it is worth getting a good guide to the camera. I particularly like Thom Hogan's electronic guide to Z cameras. It's full of insights and I recommend it highly. His discussion of the D8 setting (starting on p. 751) is quite helpful. To show that you are hardly alone, Hogan starts the section with the statement "This is a tricky function."
This is a general reply to the original question - I have both the D850 and the Z 7. I bought the Z 7 last September and have taken thousands of pictures with it since then using both Z-mount lenses and F-mount lenses (with adapter). Both of the cameras are exceptionally well made, high-end cameras and you won't be disappointed with either. The bodies are both about the same cost. But they have different strengths. My wife and I specialize in theater and performance photography (often in low light) and we do portraiture, events, and take on a variety of assignments for area magazines. Most of our work is hand held, so weight is a factor. We rarely photograph birds-in-flight or sports. If these were my interests, the D850 would be the clear choice. But its weight is a liability for me, making it no fun to travel with or carry around for long periods. The Z is a very solid camera, smaller and lighter than the D850. And it is much easier to carry for long periods and travel with. The smaller size has caused Nikon to remove some of the buttons on the body, meaning you need to use the menu for some controls (like formatting the card)--a minor inconvenience. The Z also has only one card slot (the D850 has two). Both use the XQD card which is very fast and excellent, though pricey. (The D850s second slot is for an SD card.) When the Z 7 was first issued, people complained about the single slot, but I simply carry a back-up card for emergencies. The Z cameras use the new larger diameter and short flanged Z-mount lenses. Only a few lenses have been released so far, but they are all excellent. (The 24 - 70 f/2.8 is my favorite 24 - 70 zoom of all I've used, but it's not cheap.) You can use any recent Nikon F-mount lenses with the use of the FTZ adapter (recently included in the purchase price) without loss of quality. Nikon engineers claim that the Z-mount lenses offer design advantages and I believe them, but understanding why is above my pay grade. Finally, I should mention that the focus module for the Z series cameras is different from Nikon's DSLRs. There is something of a learning curve to mastering it. I'm pretty comfortable with it now, but that wasn't the case when I first acquired the camera. Overall, my own opinion is the Z 6 and Z 7 point the way to the future. The next mirrorless cameras that Nikon releases will no doubt address some of the quirks of these initial offerings. But all things considered, the Z 7 is a great camera as it stands now and I find that I'm using it most of the time when given the choice.
My wife and I are theater photographers (we use Nikons, the D500 includied). In the theater, the light is constantly changing, so we prefer to shoot in manual (exposure and shutter speed), but we set our ISO to automatically change. Works extremely well. (You have to decide what the max ISO will be. We'll set it for ISO 12,800, although you may want to set it a bit lower for the D500. Try ISO 8000 as the max.)
Good luck.
I think that you are getting many viable suggestions to your questions about which lens to use. The 35 - 70mm was a good lens in its day, but covers a very narrow zoom range if you are seeking a single lens. Plus the D850 will not make your copy a better or faster focusing lens. The D850 is such a high resolution camera that it tends to magnify any weaknesses that lenses have. You can't go wrong with Nikon's 24 - 70mm f/2.8 (either version). As mentioned above, the new version is slightly crisper at the edges and has VR, making it a heavy lens. It's also pricey. I'd actually like to second the suggestion that you try the Tamron 24 - 70 f/2.8 (second generation). It is MUCH less expensive than the Nikon and you don't lose much in the way of quality. It has vibration reduction (which Tamron labels VC). It is sharp and has excellent contrast. I've also had good luck with Tamron service. Good luck.
Depending on the kind of photography you do and the gear that you want to move around, rolling cases can be invaluable. We wouldn't be without them and have used them for years. The excellent quality bags by Think Tank (that other people have pointed out) are particularly good. Many although not all of the bags will fit in an overhead compartment for a domestic flight. My wife (also a photographer) and I particularly like 4 wheeled bags -- often referred to as spinners -- they move easily and you can roll them down airplane aisles and other places where two wheeled bags won't go. You lose a bit of space, but for us it's worth the trade off. Excellent spinners can be found from Think Tank (Roller Derby), Lowepro (Photostream SP200), Vanguard (Alta Fly 58T), Manfrotto (2 pretty new models), and perhaps others. The best made of these are pricey -- between $300 and $400. Slightly less expensive is the Lowepro at just under $300. The Vanguard is the least expensive, but I've not seen it, so can't comment. Good luck.