I've never had a portable mp3/video player, but loads of my friends have and they've never had any complaints about iPods, but one a friend of mine had a Sony and he said it was quite crap and another friend was not very pleased with his Creative player. Can't remember what his complaint was, but he was seriously thinking of going back to being an iPod user.
But as I've never owned one myself, I can't really know.
As for the screen on the iPhone getting greasy, that is a real problem. But I guess you can solve that easily by using one of those monitor wipes every now and then.
The high end Nokias(for example) do seem to have pretty good mp3 players in them(as well as using internet and some other features), though. Same quite propably goes Sony Ericssons too. So because Apple had zero experience of making a mobilephone, I'm a little sceptical about iPhone working as a phone. I could be wrong, though.