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I know Zeetes would be mad at me, but I prefer Bushmills over Jameson, especially if you don't like alcohol taste. Bushmills white label is very mild and smooth, especially with ice.
Yeah, Irish is probably the mildest whisky to start with. And I didnt' think about the Ice vs. neat issue. I still have a hard time drinking most whiskey totally neat. I can drink Abelour and Macallan neat pretty easy, but I find it difficult with Bourbon. But, I will do it every so often to try to really taste the flavors.
However, if I just want to have a few drinks and not concentrate on it too much, I usually put a very small piece of ice in each 1 1/2 ounce drink. I find it helps bring out some flavors and rounds off the bite bit.
What I have stopped doing is throwing a bunch of ice in because you end up with whiskey flavoured water.