Obtaining Your Pokérogue Pokémon!

Catching Pokemon works the same as in the original games. However, the catch rates are more generous in Pokerogue. You can safely catch many early encounters without weakening the Pokemon first.

There are two ways to obtain Pokemon: catching them and hatching from eggs.

Hatching Eggs

There 5 tiers of egg: Normal, Rare, Epic, Legendary, and Manaphy. The Pokémon found in each Egg tier depends on that Pokémon's base starter cost.

A Pokémon that costs 1-3 points is found in Common Eggs, a 4-5 cost is Rare Egg, 6-7 cost is an Epic Egg, and an 8-10 cost is a Legendary Egg. Manaphy Eggs are special as they only contain Manaphy or Phione, of which there is a 1/8 chance to get Manaphy or a 7/8 chance to get Phione.

To hatch an Egg, you need to complete waves in any mode. The waves do not have to be done in a row, so losing a run does not reset progress on hatching eggs. You need to complete 10 waves to hatch a Common Egg, 25 waves to hatch a Rare Egg, 50 waves for Epic and Manaphy Eggs, and 100 waves for a Legendary Egg.

When an Egg hatches, you will be able to use that Pokémon as a starter in future runs. Hatched Pokémon will not be added to the party of your current run. Hatched Pokémon also come with an egg move and each Pokémon has 4 of them, 3 common moves and 1 rare move.

It is possible to get a duplicate egg move when hatching a Pokémon you already have. When getting a duplicate egg move, nothing is gained and the text box that normally announces new egg moves is skipped.

You can have up to 99 Eggs at once and all Eggs progress through their required waves counts at the same time.

Pokérogue Vouchers

What are Vouchers?

There are 4 different types of Vouchers: a regular Egg Voucher which gets you one Egg, an Egg Voucher Plus which gets you five eggs, an Egg Voucher Premium which gets you 10 eggs and one guaranteed Rare Egg, and an Egg Voucher Gold which gets you 25 eggs and one guaranteed Epic Egg.

How to get Vouchers

Defeating a new Gym Leader or Elite 4 member for the first time will give you an Egg Voucher Plus, and all subsequent defeats of that specific Gym Leader or Elite 4 member will give you a regular Egg Voucher.

Defeating a new Champion for the first time will give you an Egg Voucher Premium, and all subsequent defeats of that specific Champion will give you a regular Egg Voucher.

Completing Classic Mode for the first time will give you an Egg Voucher Gold, and all subsequent completions will give you an Egg Voucher Premium.

Completing the Daily Run for the first time that day will grant you an Egg Voucher Premium. Subsequent completions of already completed Daily Runs grant no additional Egg Vouchers

Some Obtaining Pokemon Tips

You can get eggs from the Egg Gacha (in the menu) using Egg Vouchers. You get Egg Vouchers from beating Gym Leaders, beating Classic Mode, beating Daily Challenges, every 50 stages of endless mode, and occasionally in the item shop. You get higher-roll vouchers the first time you beat a Gym Trainer and beat Classic Mode.

I recommend the Legendary Gacha until you get your first Epic or Legendary Egg. Then, switch to the Shiny Gacha.
You have a higher chance of getting high-rarity items based on the number of shiny Pokemon in your team. The Shiny rate from the Shiny Egg machine is 1/64 and 1/128 from the other machines.
Eggs hatch after a certain number of battles (based on their rarity).
Every Pokemon (except Ditto and Smeargle and has four possible "egg moves" unlocked by hatching it. One of the moves is rarer (and usually) better than the other three. Egg moves range from earlier unlocks of level-up moves to powerful moves usually reserved for Legendary Pokemon.
You get Candies (like in Pokemon GO) every time you catch or hatch a Pokemon. You can use these to either reduce the cost or unlock passive abilities for starter Pokemon. Passive abilities don't overwrite the Pokemon's normal abilities.
I suggest catching a lot of Zigzagoon/Linoone, Magikarp/Gyrados, and copies of any Shiny Pokemon you have. Use the Candies to reduce their cost as low as possible. Zigzagoon is the lowest-cost Pokemon with Pickup, Gyrados is a good late-run Pokemon, and shinies get you better item choices.