Hello Arseylah, I see you've already gotten your first pets.
There are many things to do on res, a lot of players collect pets for instance. You can start by taking a look at the Help page on the Navigation menu on the left of the screen, it answers many questions that new players ask.
Collecting pets is one of the most common goals here, everyone wants to collect their favourite colours, Credit Shop pets and more. You can find the list of all the pets by Going to the Hatchery, and there is a link at the top that says Creatu List, giving all the creatu and where they can be found.
Some creatu can only be found at certain times of the year, and others are found year round. The rarity is listed in percentages, the lower the % is the rarer the creatu. Most of the ones listed in "Other" are found in the credit shop, but these are rotated out regulary so that the eggs only one or two of the creatu are there each month. Some are retired all together so you can only get them by buyinf from other players.
If you have any more questions you can rmail me or a staff member :) But i recommend reading Help first as it will clear up many things for you.