Choosing your own tarot deck is a very personal thing; every deck "feels" different to every person. You should choose the deck whose images really speak to you.
There are debates about owning more than one deck. I personally own four decks -- the Rider-Waite, the Robin Wood, the Norse, and the Cat People tarots. Many experienced readers feel that in owning more that one deck you are "collecting" them, thereby degrading the personal nature of the tarot. However, I enjoy the artwork of many tarot decks and like to own them for aesthetic reasons.
The Rider-Waite deck was my first tarot deck; after three years of using it, I felt that I needed to "graduate" to another deck, although the Rider-Waite is a fine tarot deck. I went in search of one, looking carefully at each available deck. I saw the Cat People tarot and felt it was the one for me.
I bought the deck and happily took it home, but when I began reading with it, I discovered I drew complete blanks looking at the cards; the meanings were not coming to me at all. I loved the artwork of the Cat People tarot, but realised that it was not the deck for me.
I went back to the Rider-Waite until I could find another deck that I would really connect with. I finally found it in the Robin Wood tarot, a deck that jumped up and grabbed me. This is the deck I use for almost all of my readings.
Meanwhile, I had been eyeing the Norse Tarot, an expensive but wonderful deck. I finally decided to buy it after a lot of thought. My family is originally from Norway and I've always felt a deep connection with the Norse tradition, so the Norse Tarot really appealed to me personally. I use this deck only when I have big questions, or when, for some reason, I just feel that I should use that deck. It is not a deck for trivial matters, as it tends to "tell" you when you use it.
The best way to pick your own deck is to find a store in your area that sells many different decks. New Age and metaphysical bookstores are more likely to have a good selection on hand, although many chain bookstores do carry the more popular ones, such as the Rider-Waite, and will be glad to special order any of the other decks.
When you visit the store, ask if they have representative pictures of each of the decks. Some stores will let you look at a deck from the box, but I have a warning note here: if you do not know much about the tarot, you may not think this is a big deal, but many tarot readers will not buy a deck that has been handled by others. A deck is a personal thing, and many tarot readers believe that their decks take on something of themselves. Personally, I do not mind a deck that has been "handled", and I always let interested people look at my decks. I figure that if I have had the deck long enough, no one is going to take away that personal touch in the deck. I have seen one store whose handling of tarot decks I really liked (The Stone Lion, in Ft. Collins, CO); they had a 3-ring binder where each page had four cards from all the decks they carried. This way you could really get a good look at the deck without opening a new one. Even the lady behind the counter said they did that because the tarot deck is very personal, and this isn't even a metaphysical bookstore!
Whether you are looking at a folder or the deck itself, look carefully at each card. Some decks will appeal to you, others will give you no feeling at all. You want a deck that is going to jump up and really grab you.
A friend of mine recently decided that she wanted to start reading the tarot. She didn't know what deck she wanted; in fact, she had only ever really seen about two decks. We went to the Stone Lion Bookstore in downtown Ft. Collins, Colorado and looked at their folder of decks. They had about 20 different decks in this folder, with four cards from each deck. We started from the beginning and she looked carefully at each page. Every once in a while she would see a deck that caught her eye and would say, "that's a nice one...we'll keep this one in mind." Finally, after about 15 decks, she turned the page to the Arcus Arcanum deck, and practically shouted, "THAT'S THE ONE!" The deck had just about grabbed her! That was the deck she chose, and she does a very good job with it.
Not every person can read with every deck, just as I said about me and the Cat People tarot. Each deck is personal. My friend can read extremely well with the Arcus Arcanum deck because the images really speak to her. I, however, look at the deck and see some very nice artwork, but I have trouble reading any meaning in the cards, because the deck isn't "my" deck. I cannot read any meanings in the Cat People tarot, but I have met people who swear by this deck and are excellent with it.
If someone tells you that a certain deck isn't good to read with, you shouldn't take their word for it; check the tarot deck out for yourself. You might surprise them.