How lightweight the install becomes depends on what packages you choose.
If you want a live CD then I'd suggest CentOS. It isn't the most modern desktop but it's one of the cleanest. It's perfect for use as a server/workstation.
Otherwise you could use Mint Linux. It's Debian based, and light and easy.
You'll have to install PHPmyAdmin manually though, but it's just a matter of unzipping a directory.
If you just want a LAMP server, then instead of installing L(linux) A(apache) M(mysql) P(php), you could try using WAMP (Windows AMP).
I use Uniserver, and it's fast and does everything my Linux box does.