No such thing as a "double malt." Just because there is a "single malt" doesn't mean there are doubles or triples, etc.
The more common types are:
Single malt - this is a whisky that's made exclusively of malted barley, at only one distillery, and not blended with anything else.
Vatted malt (sometimes called pure malt) - is a blend of single malts, not necessarily from the same distillery.
Blended - this is a blend of malt whiskies and grain whiskies. Distilleries that make malt whisky don't usually do both malt *and* grain (such as rye, corn, etc) but some do. Blended whiskies are various combinations of malt and grain, usually from a variety of distilleries.
Blends vary in character and quality, but are made in such a fashion that their flavor is consistent year after year. Vatted malts are also more consistent due to the blending of various malt whiskies to make the final result consistent. Single malts are more unique, and while each distillery has its own signature flavor (from strong or harsh, to mellow and subtle, and everywhere in between), every year is different and can result in noticeably different whiskies from one year to the next. A lot of the higher end single malts will not only have an age statement (how many years aged in wooden casks) but also the year it was made.
A good range of single malts will fit your budget, and something in the neighborhood of 18-25 years old might go over really well. Macallan is always a good safe bet. If you want to show you care, avoid Glenlivet or Glenfiddich (neither are *bad*, just common and unremarkable in comparison). Bowmore and Ardberd are both very good.
For a blended whisky, Johnny Walker is very commonly known, but they make a variety of blends that range in qualtiy. Red is the common, every day style. Black is a little better. Gold is good and within your price range. Blue is their top of the line blend which runs around $200 (all of the whiskies in this blend are over 25 years old).