I have yet to find the ideal website. Rapidweaver did odd things with text so that what was lined up properly on my screen would overlap on other peoples' computers. Smugmug had been unattractive a few years ago, the site I had developed professionally looked good and worked well - but loading images is a pain (Joomla).
I now have the vast majority of my images at Smugmug and my newer images at this gallery.
The images are larger than ever before, and when you click on the images, can be seen on their own, with no thumbnails occupying half the screen. You can go through the images via the keyboard, using the left and right arrows.
I haven't found a convenient way to make Smugmug do everything I have on my website (eg. downloading pdf's) so for now, it's just a way to look at images conveniently.