I use more than one deck, depending on the nature of the reading. Also bear in mind that in some cases the artwork itself may be what is relevant, rather than the official meaning of the card. For example, the Stars card in the Native American deck shows a spider on a web whose intersections are marked with stars, so as well as its official meaning (proper balance of physical and spiritual elements) it also comes up for things having to do with astronomy, electronics and the internet.
Native American Tarot Deck by Magda Weck Gonzalez and J.A. Gonzalez
This deck uses symbolism from several native nations to describe various attitudes, behaviours and states of being. The meanings of the Major Arcana cards are quite eccentric and these Major cards do not have reversed meanings, instead containing both good and bad aspects within themselves. The suits are Blades (tomahawks), Pipes (tobacco for the ceremonial smoking of), Vessels (clay jars) and Shields. The artwork is underwhelming but this is a powerful deck. Many modern, non-standard decks have been bowdlerised so that it's impossible to get a bad reading from them, but I always say this deck doesn't so much do character assessments as character assassinations. At least that way, if it tells you something nice you know it means it.
The Arthurian Tarot by Caítlín and John Matthews
This deck is beautiful to look at, with a lot of symbolism contained in the artwork. It is based around Mediaeval mythology about Arthur and about the mystical underpinnings of Britain, and leans very heavily on the idea of liminal space between this world and the Otherworld. The suits are Swords (Air, Spring), Spears (Fire, Summer), Grails (Water, Autumn) and Stones (Earth, Winter), and are based on four of the traditional Hallows (holy objects) of Britain - the Glaive or Sword of Light (or the Sword of Nuadu), the Spear (sometimes said to be the one which pierced Christ's side on the Cross), the Holy Grail and the stone Gwyddbwyll (or Fidchell) board, a kind of 7x7 chessboard whose name means "wood-cunning", and which represents the land. The cards do not have reversed meanings, instead containing both good and bad aspects within themselves.
The Morgan-Greer Tarot William F. Greer and Lloyd Morgan
An attractive take on the standard Rider-Waite-style Tarot deck, with suits of Rods, Cups, Pentacles and Swords, and upright and reverse meanings for all cards.