At the end of the day, I recommend figuring out your preferred distro if you haven't already and going from there. Most major distributions like Ubuntu, openSuSE, and Fedora have Raspberry Pi versions.
If you're asking for optimizations, you'll find them in keeping as few processes running as possible, and you may get better speeds by hardware means such as purchasing a micro SD card with faster read-write capability or getting a cooling fan for the CPU.
Hope that helps, and props to making and running your own website from home! :)
If it is the 8G version, it might be worth implementing a ramdisk for the web server and web logging directories. That way the sdram doesn't get trashed as quickly, and response will be quicker.
I would install the minimal Raspbian and then add the server applications you want. Also, don't forget you can completely shut off the HDMI for a tiny bit of power savings. If you are going to use https, every little bit counts.
The only reason I actually name a distro when normally I'm hugely agnostic, is because Raspbian is the official distro for Raspberry Pi, and therefor can always be expected to support rpi's various idiosyncrasies.
Then again, I may be completely insane, because I'm humming and hawing around building a Single System Image out of a pair of them and actually making something roughly analogous to a laptop to go along with it.
To be frank, you probably shouldn't take my advice. I'm clearly a glutton for punishment, and it may lead you to the darker corners of computing related insanity.
I used Raspbian (*versions wernt important), mainly I'd choose a distro that works for the versions of server software that you want to keep updated (i.e. older=Ubuntu, newer=Linux Mint)
Anyhow, I think I will try again. Any advise or gotchas I should be aware of before embarking?