What is the best website solution for a photographer?

You could have a look at SmugMug and Zenfolio.

I was pretty much in the same situation a few years ago and at that time SmugMug was the most compelling, flexible and still reasonable solution. You can easily integrate it within a personal domain / website.
Those services are not free so to compare things fairly you should check also the paid version of other solution like 500px for example.

My experience with Smugmug over the last couple of years has been flawless.

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