I have several varieties of absinthe in my liquor cabinet. Lucid is the most commonly found brand and it's not bad to start out on. Better brands include
Delaware Phoenix, a micro distillery in New York, and Mansinthe (Marilyn Manson's commissioned absinthe). Kubler is quite good, too.
Avoid the brands from eastern Europe--those tend to be fakes, made from grain alcohol with infused botanicals. Tourment comes to mind, but there are many others to avoid. Also, be aware that Pernod does not make true absinthe anymore, just pastis. If you just ask for "Pernod" in the store, you will get pastis. The difference: pastis is an anise-flavored liqueur, which has added sugar, but no wormwood. Absinthe is distilled from a mash containing several botanicals, including grand wormwood and anise. No sugar added.
Absinthe was banned in the early 1900s, primarily due to lobbying from the wine industry, which saw it as a threat. The fact that the drink was popular with a bohemian crowd didn't help its image. The stories of absinthe-fueled lunacy and crime were completely fabricated, and prime examples of the yellow journalism that was common in the day. I believe it was banned first in France, then a few other European nations followed suit, then the U.S. The U.S. ban was lifted in about 2007, allowing a limit of 10 ppm thujone. Some absinthes sold in Europe may have thujone levels up around 35 ppm. The toxic threshold of thujone is orders of magnitude higher; you won't hallucinate from absinthe.