No linux has a built in webserver. Most distributions have webservers installed by default, or available for download.
What is "best" is a matter of opinion and of what factors are important to you in a webserver. Majority opinion (at least by usage) seems to favour Apache 2, which is available for all Linux distributions. If you want to make it best for your purposes you should download the source, configure it to your exact requirements, and compile it for your system.
Try RHEL 5.4, cent os 5.4, or fedora 11/12 and click on "server" on the package selection screen.
Or if you're already familiar with Linux debian's good and Ubuntu server ain't bad either.
On redhat based systems, like RHEL 5.4, cent os 5.4, or fedora 11/12, you'll be able to use yum to easily customize your apache, apache modules, php, mysql, etc without having to compile from source.
If you're looking for something very specialized then you should look into compiling from source as ijack suggested. There's a learning curve, compiling is harder than using yum, rpm and apt-get, dpkg.