A tasting implies marked contrast, but the question is how much contrast will remain enjoyable. The preference for Glenlivet 12 is a bit of an enigma, not that it's a bad whisky or anything (I do drink and enjoy it), but simply that it is so subdued in character that it is difficult to guess how much peat and smoke you will want to embrace. If you will notice however that the "rich" side of the chart is populated by the majority of the world's most expensive scotches, I think we can conclude that is a safe direction of travel. Personally I would counsel against Ardberg 10 if you are not very experienced with scotch, as its smoky qualities can be overbearing. Laphroaig 10 could be a better choice along those lines, especially if you plan to add a small amount of water in the traditional Scottish style, which will bring out its sweet and mild character and tone down the smoke. This would be my "perfect" 3 malt tasting for a novice on a budget (omitting blends):
1. Macallan 12 with water
2. Laphroaig 10 with water
3. Lagavulin 16 that has been allowed to stand with ice
4. Macallan 12 neat
5. Lagavulin 16 with water
6. Laphroaig 10 neat
7. Lagavulin 16 neat
If Lagavulin is judged too bold you could substitute Highland Park 12, which is also well regarded.