As you start the game, you will be given 3 free initial dragons as starters.

1. Fire Element Dragon

2. Wind Element Dragon

3. Earth Element Dragon

As of now, the game have 7 different dragon elements as shown below. And the only way to get other type of dragon is breeding. 

Getting ember for from the ember mission and using them during breeding. Breeding process of dragons other than the initial free dragon (Parent Dragon) goes like this : (i.e.)

Parent Dragon 1 : Earth

Parent Dragon 2 : Air

Ember :  Electric

Element of the Resulting dragon will be : 40% chance Earth , 40% chance Air, 20% chance Electric

NOTE : In case the element of the chosen ember is different to both of the parent's dragons, and the element of the new dragon is the same as the chosen ember, the resulting dragon will end up with the new element (different to those of its creators), but, it will end up as a “basic dragon” (Common rarity, with a total sum of stats of 30) no matter the rarity or stats of the creator's dragons.

With this, if you want to get another element of dragon, you should do it as early as possible (which is on the 1st breeding or 2nd breeding process on of common dragons). This will reduce waste on CYT and embers if you do it on the latter process ended up with Stats of 30.  

Just like Pokemon, taking advantage of the elements that you will be using and including to your team during PVP and PVE is a major keypoint. Deciding for what type of elements you will go for, you should decide as soon as you start playing. And making a plan for the breeding process, taking the stats into consideration will also a good one. 

As of now, there are only 7 elements of dragons, but according to the Whitepaper, they plan to add 2 new elements each year. Which will be a good point on changing your strat towards the game. And making the game more challenging as well since new element means new strat competition.