tiny voices :
I would not go mITX for a budget build. You can get a much cheaper and almost as small mATX build which will leave you more money for a better GPu.
He doesn't have a monitor at home which is why I suggested to go with a mITX build. The way his tv is set up is that he has a a book case which is close to a fireplace with the tv mounted above it.The PC would need to fit within a shelf of the book case, so it's likely a mATX case wouldn't fit (at least from what I can remember).
I'll have to check with him tomorrow on the length/ depth of the shelves.