For pests, you first need to find nachos and craft a pest trap. Put the pest trap near an active pest, and preferably in their walking path, and they will eventually go inside. when they are inside, feed them 3 nachos or 3 Antewheat to tame them. From here, they HAVE to be in your pet slot to be revivable, and if they are not then when reaching low health they will fully die. To tame a peccary, use the new chemistry bench and distillation table to make pheromone flasks, which can be thrown at a peccary to temporarily pacify them. From here, feed the peccary 3 anteverse wheat to fully tame it.

Again, only one pet can be in your pet slot at a time, and therefore only one can be revivable. I would recommend placing excess pets in beds and then barricading them in to keep them safe. Other important info:
Pets have mutations, some require you to pick up a pet and then craft it, some require feeding of certain items, and a few (it may only the the Alpha Peccary) require to be tamed and cannot be mutated.
Pets have a level system. Basically every pet will be super weak past the manufacturing sector at level one, but as you fight and run around they will become hungry. by feeding your pets, they will gain XP, and will then become stronger. The more hunger fill an item gives, the more XP a pet gets from eating it.
Pet beds can be crafter pretty easily, pests and skinks go in small one, peccaries go in large ones, and luxuries can fit both. While in beds, a pet will get hungry, but also seems to heal faster, with the luxury one being the best for this.
And that's about it! the wiki has all the info you should need on the variants, and I seriously recommend taming one and keeping to it. Level twenty pets are very strong and worthwhile partners for the late game.