Ah, the dragon element. It’s a difficult type to specialize in at first, but with patience, dragon tamers can become among the most fearsome trainers in existence.
But first, a note about your likely starter. Outside of the Kalos region, which boasts an unusually high population of dragon pokémon, dragon-types are extremely difficult to find for good reason. The dragon type is one of only three element classifications that refers to the dispositions of its bearers as well as its offensive and defensive advantages and weaknesses. (The other two are the bug and fairy types.) That is to say, dragon-type pokémon aren’t just pokémon with a specific set of strengths and weaknesses. They’re also pokémon who are bestial in nature. They avoid human contact, and they’re notoriously difficult to tame in earlier stages (and sometimes, especially in the cases of the Unova dragons, later stages as well).
More importantly, yes, they’re extremely rare, which in turn means your starter may be the only dragon you’ll own for quite some time (unless, again, you live in Kalos). Hunting for dragon-types is time-consuming, and it frequently requires a lot of skill and experience from trainers who wish to do it because of the extreme locations dragons tend to nest. It’s best to train your starter for a long while, perhaps in combination with pokémon of other types, until you build up the skill and strength you need look for more dragons to tame.
Of course, there are certainly dragons you can acquire via other means. Swablu, for example, are common to the Hoennian and Kalosean mountains, and they evolve into the dragon-type altaria. Likewise, horsea, with enough time or a good friend to help you, may one day become the formidable kingdra. It would certainly be a good idea to obtain and train these, although they may still require some patience on your part—swablu because they’re not particularly strong pokémon at first, and horsea because seadra can be rather temperamental.
Which, of course, leads to the other warning that many dragons are either not very strong at first or very difficult to handle. Dratini, for example, can only learn weaker moves such as Wrap or Twister until they grow closer to evolution. Bagon, meanwhile, learn stronger moves but tend to break out into tantrums or ignore orders in favor of finding places to train itself to fly. In this sense, even if you catch a dragon, you may find that you must still be patient in order to help your pokémon to grow.
Then, of course, there are the other, smaller issues to take into consideration. For example, dragons should not be exposed to cold temperatures for long periods of time (although a few species can handle cold water), most of them rely on a strictly carnivorous diet, dragons need a lot of space (making settling down a difficult prospect for some tamers), always acclimate new dragons with your old ones (meaning ease new catches in with your former team to avoid in-fighting), and never handle your dragons and eat without washing your hands in between (as some dragons may carry salmonella).
This all isn’t to discourage you from launching into a career as a dragon tamer, anonymous. It’s more to say that the biggest advice I can offer anyone who wishes to become one is that the profession takes a lot of patience, courage, and understanding of your element. It’s no wonder why dragon tamers are famous for being dedicated to their craft. While, certainly, specializing in any type requires a full understanding of that element, the dragon type requires a lot more attention to the details outlined in your pokédex.
However, as I’ve noted earlier, it’s ultimately a rewarding experience. Out of all the type specialists in existence, dragon tamers are known for having the most colorful stories attached to their adventures—with good reason as well, given how difficult it is to find dragons in the first place. Likewise, dragons tend to evolve into some of the most powerful and intelligent species of pokémon in existence, some of which rival humans in terms of wisdom. If you’re successful at raising a dragon to its most advanced level, you will find yourself with some of the closest companions a trainer can ever have.
So even if the task itself is daunting and sometimes even dangerous, never give up, trainer. In the end, all of the adventures you’ll have and all of the bonds you’ll forge with your dragons will be worth everything, including the possible case of salmonella poisoning.