Personally, I love the pathos in "Father's Day." It's probably my favorite episode from that season (although "Dalek" provides some stiff competition).
While a lot of people aren't very fond of the Slitheen, I would still recommend "Aliens of London"/"World War III." Those episodes do contain vital exploration of the concept of what it means to be the Doctor's companion. Plus, those episodes do a great job of rehabilitating Mickey. He was unbelievably lame in "Rose" yet turned into a pretty cool companion in Season 2. "Aliens of London"/"World War III" do a fantastic job of explaining how. Plus, I love the interactions between the Doctor & Jackie here. ("900 years and I've never been slapped by anyone's mother.")
If I had to pick 5 episodes from Season 1 to start out with, they would probably be "Rose," "End of the World," "Aliens of London," "World War III," & "Dalek." (I'd skip over "The Unquiet Dead" unless I knew that these folks were Charles Dickens fans to begin with.)
But I suppose some of it depends upon whether we're talking about people who need to see stuff in order in order to get it. While "Rose" is kinda vital as the series premiere, it's not necessarily too vital so long as you (a) already have a passing familiarity with the concept of Doctor Who and (b) don't give a smeg about Rose's storyline.
Now, if I was just trying to sell someone on the series without necessarily needing to spoonfeed them information about the story arc, the 1st 5 episodes I would probably prescribe are "End of the World," "Dalek," "Father's Day," "The Empty Child," "The Doctor Dances."
"End of the World" isn't necessarily my favorite episode but it is a very archetypal Doctor Who story. How someone reacts to this episode will probably tell you a great deal about how they'll react to the entire series.
Also, even if it's out of order, try to see if you can sneak "Blink" into there as well.