Oh man,
@Needa you are opening up pandoras box with this question.
Short answer - smallish backpack with good construction and weather protection, skip the sling and no screen protector.
Long answer - *takes a deep breath...
I have been on the hunt for a perfect carry option for quite some time. Over the last couple of years, I've accumulated quite a number of bags, mostly from Peak Design. They are on the pricy side but they are extremely well constructed and keep the weather out, (ask me how I know) and I don't think there is a better brand with better options IMO. Every single one that I have is perfect for me, (except maybe one) for a specific carry need. I started with slings, I got the 6l and 10l. The 6l can carry a camera with lens attached and an extra smaller lens. There's still a little room for extra bits and bobs as well as a tablet. If I have to carry a bag but want to stay as light as possible, this is my go to. No matter how much you try to cram in this bag, it only fits so much so it only gets so heavy. This most likely will not work with your proposed carry needs. The 10l carries more, but you need to be careful. If you load it up to max like I did with a Z7ii, 24-70f4, 14-30f4 and a 70-200 f2.8, (I think I snuck a 50 f1.8 in there too) with all the bits and bobs, the bag becomes extremely uncomfortable hanging off one shoulder after a short period of time. Just because it CAN fit doesn't mean it SHOULD fit. Pack accordingly. There's also a spot for a small laptop in the 10l. This sling should work for you with a possible layout being the 24-120 attached to the body, lens pointed down and 70-200 vertical on the other size of the divider with room for more if needed, just heed the advice above. After that, I got a good price on a used 15l messenger bag. I think they're discontinued at this point but it's basically an oversized sling/briefcase kind of thing with a flap with magnetic closures instead of zips. It's my least favorite but holds the stuff I tried cramming into the 10l just a little better but there's still the issue of hanging all that weight off one shoulder. I can't describe the back pain I had the next day after a full day toting this thing around. Ugh. I've heard pro's sing the praise of this bag, I just think the 10l does it better. Then I purchased the 45L travel backpack with a couple small camera inserts, a medium camera insert and a large camera insert. I LOVE that backpack! It carries everything I need with ease, especially with the excellent modular inserts. It has easy access side zips to quickly get to your gear or you can open it from the back or the front to see everything at once. I like the hip belt on this bag too since fully loaded, it can get heavy. The padded hip belt has a very clever hiding spot when its not needed. Very easy to deploy and stow on the run. There's storage spots all over this bag including for a full size laptop. It's what I use for my camera gear when I fly because it's big enough to fit everything and small enough (just barely) to be my carry on. It's just a bit too big for every day carry though, even for me at 6'-5" 250#. If you plan on traveling a bunch, especially by plane, this is probably the best option. Then I purchased the 65l duffelpack. That's great for long car trips where I don't need to worry about space or weight like I do when flying. I usually carry my camera gear (those camera inserts work in this bag too) as well as clothing in this bag and toss a sling in there too so I don't have to carry this behemoth of a bag everywhere I go when I get there, (but there's also a hidden padded hip belt on this bag too if you find you do need to carry a bunch around). It's also a great bag to cram all my lighting stuff in when multiple bags are needed, especially since it can be carried like a backpack or a duffel bag. Most recently, I got a 30l everyday backpack v2. This is the closest I've come to the "goldilocks" of bags and probably the one I'd suggest to you if big bags aren't your thing and a sling may be too small. I can carry a body or two, a speedlight, a prime lens, 24-120f4, 14-30f4, 70-200f2.8 (even attached to a body!) as well as my 400f4.5 and 2x converter at the same time. There's a spot for a full size laptop, ample room for rocket blower, spare batts, filters, etc. The side zips are awesome on this bag and allows very easy access. It can get heavier than the 10l sling, but since the weight is distributed on both shoulders, it's much easier on those long days carrying your gear everywhere you go and its a little more compact than the 45l. That is, walking through crowded areas is much easier with this bag. The 45l pokes out further and can knock people over just by turning around. No hip belt for the 30l but it can be purchased separately if needed. Fully loaded with the above is the only reason I would want a hip belt for this bag but since I don't use this bag fully loaded, its not necessary for my needs. I will say that the 45l feels more secure, you can literally lock it down. The 30l has a flap that can not be locked and although they say its weather protected, it's a flap, (with a magnetic closure latch that's pretty secure really) that can be moved out of place easier than zips. I will not be taking this bag on my snowboarding trips but I wouldn't feel too bad getting stuck in a sprinkle walking through downtown, if that makes sense. This bag has become my everyday carry. I use it as a laptop bag that I can also bring my camera and a lens or two and still have space for whatever I might find throughout the day.
For the screen protectors, I don't buy them for my cameras. I bought one of my cameras used and it had a screen protector already on it. I didn't notice any difference. First thing I do when I get a new phone is put a screen protector on it. That thing gets dropped, kicked, thrown, slid on surfaces and slipped in pockets daily. But I don't treat my camera like that .
Sorry for the long winded response. Hope you can gain something from it though.