And I am not talking about using different frameworks / compiled languages / etc... I'm talking about the improved techniques we've developed over the years combined with new features in browsers, such as:
* HTML5 vs. HTML4 (streamlined and more consistent syntax in a lot of places)
* Float-based grid systems for layout
* Flexbox(!) for alignment
* media queries and picture/srcset for responsive design (heck, the whole concept of responsive design)
* web fonts (not being limited to the dozen or so that are available through the OS only)
* BEM methodology (having a modular mindset about styling components, combined with avoiding specificity issues by just using a class for everything)
...and that's just plain old HTML and CSS... don't even get me started about javascript (even just JS/ES5!)
Why are you assuming said website needs to be successful on the market? Maybe it's a personal website or a hobby project.
If I were starting now, my inspiration would possibly be things like: responsive, single-page apps, with ajax, websockets, etc.
I was going everywhere and viewing source and you could basically figure out how everything was made. Now--not so much.
It's not so much 'success' as similarity with popular projects.
http://arachnoid.com/arachnophilia/index.php
(Pleasantly surprised to see this is still going strong after 20+ years.)