Ice cubes (and anything cold, for that matter) "numbs" the flavour of the drink, so for those who are a bit unsure of whether they like scotch or not, it might be a good way of easing yourself in. The splash of (room temperature) water does the opposite, it enhances the flavour, although some malts really can't take any water. You'll have to experiment with that. Do use quality bottled water, though. Tap water might contain some odors or chemicals that might ruin the taste. The recommendation is to use the same water that the distillery is using, but that's a bit extreme, I'd say...
As for some recommendations, try the more "easy" malts first. Something from Speyside, or maybe something that has been aged in a sherry cask, those tend to be a lot smoother than the "bottled smoke" from Islay. Oh, and although it isn't Scotch (it's an Irish blend), Bushmills' Black Bush is really nice. By far my favorite among the "non-scotch" stuff. It's really smooth, with a nice fruity and vanilla-like flavour.