If you found the Laphroaig a bit too much on first taste
(so did I, but I have grown to love it) then you are probably better avoiding the Ardbeg for now (even though it is my favourite of the less than 15 year old whiskies you list) as it is pretty full on too.
If you like peat already then the Talisker 18 is a stunning whisky though more expensive. Lagavulin 16 is more reasonably priced and, as Jan noted, is the dram that converted a number of the forum members (myself included) onto the peaty stuff.
If you don't want to go overtly peaty then the Bruichladdich 10/12 or Coal Ila 12 (many forum members have been disappointed by the 18 ) are a fine entry point.
Let us know how you get on, and welcome