You can gain eggs through completing quests or adventures, as drops from adventures, or from buying them with different currency. Eggs can drop different rarity or types of dragons.
The Egg Book in-game describes different Eggs and what they contain.
You can also check ZeTFaY's website for information on the rates of obtaining each rarity from each Egg type.
These have a chance to drop from most Adventure stages, and are the stage 4 egg reward for Normal mode.
You can also get one every day after 20 minutes of playtime for the day.
They have a slight chance of hatching Rare dragons (3%) but note they cannot hatch Light or Dark dragons.
Hatches Rare rarity dragons or above, with the same rates as summoning.
Very useful for fodder, and you occasionally get lucky with them.
You can find them in these places, to name a few:
Similar to Mysterious Eggs in what they hatch, based on element. You will mostly get these from:
Similar to Mysterious and Elemental Eggs in what they hatch.
These can only be bought with honor points earned from Colosseum.
I do not recommend buying them, as your honor points are better spent on skill slimes.
Similar to Mysterious Eggs in what they hatch and their rates, but they also have a chance of hatching a limited dragon.
The rate of hatching a Legendary is the same as Mysterious Eggs, and the chance of hatching a limited Legendary dragon is about 0.02%. Will you get lucky?
Hatches only Heroic dragons.
Miracle Eggs have a chance of hatching a limited dragon, but there are no good limited Heroic dragons as of now, so you can ignore that chance.
These are mostly event rewards, and you also gain a few from Master’s Quest.
Hatches Heroic or above dragons.
Eternal has a chance of hatching a limited dragon.
The drop rate of a Legendary dragon from these Eggs is boosted from the usual 1% to 7%.
You get 1 Eternal Egg every month from log-in bonuses, and you can also get both Eggs as clear rewards in Elemental Towers.
Hatches only Legendary dragons.
Mythical Eggs have a chance of hatching a limited dragon.
You get 2 Legendary Eggs from log-in bonuses every month.
Mythical Eggs are usually quest and Tower rewards, or you can buy them with topaz.
Hatches only limited Legendary dragons. Highly coveted.
You can buy them with Clan Coins (the usual method you will obtain them) or Valor Medals. It is not recommended to buy them with Valor, however, as for slightly more Valor Medals, you can buy any non-limited Legendary of your choice, instead of the possibility of being disappointed by an Absolute Legendary Egg.
Good luck obtaining your favourite limited!
The only thing you should be buying with amethysts.
Hatches slimes between Normal (2-star) and Legendary rarity.
They are mostly bought with amethysts but are occasionally event rewards, and you also get a few from the Elemental Towers.
These can be bought with money, topaz, or valor medals. It allows you to select one non-limited Legendary dragon of your choosing.
If buying these with real money or topaz, I suggest only buying this when you need a certain Legendary dragon immediately.
You can buy any selectable dragon from the Witch Shop, which is much cheaper. There are also other packs that might be more worthy of your money, such as Capsule Coins, which can give you many resources, and possibly one or more Legendary dragons, for the same price.
You might also pull the dragon you selected from summon, or hatch it from an Egg, at some point.
Therefore, the best use of a Legendary Selection Ticket is for when you:
If you have all of this, as well as the funds, ready for your new dragon, then I wholeheartedly support the decision to buy a Legendary Selection Ticket.
It is also recommended to use your Legendary Selection Ticket to summon a Dark or Light dragon.
Dark and Light dragons have a significantly lower chance of being summoned than other elements. This is especially important information when it comes to Mastering your dragons.
No matter what you select, there is always the chance that you will eventually summon the dragon you originally selected. If you chose an Earth, Water, or Fire element dragon, the best thing to do with the duplicate dragon would be to farewell it for enhancement points. Enhancement points are relatively easy to come by. You can get some as rewards from the Tower of Tests, or buy them with Diamonds or Clan Coins.
Even if you decide to use the duplicate dragon for Mastering your selected dragon, it is still relatively easier to come by Mastery fodder of Earth, Water or Fire elements compared to Dark and Light.
Dark and Light Mastery fodder is much harder to come by due to their lower drop rates. Whenever you get duplicates of Dark or Light dragons, or even 'bad' Dark or Light dragons with better counterparts, you will want to use them for Mastery. Thus, if you eventually summon the dragon you originally selected, you now have excellent Mastery material on your hands and nothing to regret.
That said, if you have a lot of money to spend on this game, and foresee buying the Selection Ticket multiple times, then absolutely feel free to select whatever you like. This is only advice for making the wisest choice, but the best choice is whatever makes you happy.