"Perfectly" is a high bar, and I'd not myself say that any phone reaches it.
The most important thing about mobile phone photography is the software. All phones have small sensors, most have fixed apertures, and even where they have variable apertures the short focal length means that the depth of field is still large. So if you see a phone coping with tricky lighting, producing impressive shots in low light, producing a bokeh effect, that's all down to the software. And while some of the others have come on lately, Google have the best algorithms, which points you to the Pixel series. HTC (remember them?) so still do very good cameras in their flagships, but they've so little support these days that it would be hard to recommend them. I've read a number of people saying that the Snapdragon s10s (North America, China, Japan I think) have better image processing than the Exynos models (most of the world), but I can't confirm that personally. Ports of Google's camera software are available for some other phones: the closer in hardware to the Pixels the better, but that's something you might want to consider looking into if there is a non-Google model that you favour.
Of course you should be aware that when people are discussing "best" they are sometimes nit-picking over small differences. What matters is what works for you. Tastes differ too, e.g. I prefer natural colours and will accept some noise in order to preserve detail. Others might prefer "punchy" colours and no sign of noise (at the price of smearing away details). So I'd always recommend finding some samples from any phone you are considering, ideally in a range of lighting conditions, and judging for yourself.
One thing that the Pixels won't give you (at least until this Autumn) is multiple cameras. So if having a modest telephoto is important for you that might be worth considering (you can zoom digitally, but there's always some loss of quality with that). But in those cases make sure you check samples from both cameras, since the quality of a secondary camera (ultra-wide or tele) is not always the same as the main one.
I'm afraid I know very little about gaming, other than to say that if that's important to you you want a flagship-class specification. The Snapdragon 855 SoC has the best gpu currently, so if gaming were a priority for me I'd consider that plus adequate RAM as priorities. Of course lower resolution screens are easier to drive, so this will be more important with a 2k screen than a 1080p for example.
I'm sorry that's thoughts on features rather than specific phone recommendations, but I'm not currently in the market (my phone is under 2 years old) so I'm not following specific phones as closely as I would if I were looking to upgrade. I also don't know your budget, what country you are in (some phones are different in different countries), and what your other preferences might be (bigger or smaller, flat screens or curved, etc).
