Really you can use any distrobution you want. Ubuntu, Debian, Mint, Arch, Fedora... Just install XBMC. Ask your self what distrobution are you comfortable with?
However why not just use OpenELEC on your HTPC? Unless you need a full desktop OE does most everything you could want from an HTPC.
Dish anywhere uses Adobe Flash.
I will say that OpenELEC does not come out of the box with a web browser.
http://dl.dropboxusercontent.com/u/8224157/OpenELEC-Ultra/opera/final/index.html
Opera is available as an unoffical addon on x86 and x86_64,
but not for rpi.
There is no adobe flash player for ARM devices like rpi. In fact flash has been discontinued and no longer maintained for linux (except in google chrome).
If this is a deal breaker, then you will need a distrobution like rasbian for your rpi. You can use Midori browser and "gnash" flash player. You will also have to set up XBMC seperately.
You may have a poor experience playing flash video on rpi without hardware acceleration. The CPU is very weak!
Code:
sudo apt-get install gnash
sudo apt-get install browser-plugin-gnash
sudo apt-get install xbmc