I am also doing the same thing! First, you should add every pet you don't ghave yet onto your wishlist and make sure you have (a) seperate group(s) for any doubles.
1. Adopt the maximum of all monthly pets every month. If you get duplicates of any outcomes, trade them for outcomes you don't have yet from the month. It's much easier to collect all the monthly pets during the month rather than after the month. The monthly swaps thread becomes very helpful!
2. If there is a monthly pet going for extreme overpay, take it! If someone is offering you a '12 very rare for your harder to find monthly pet, take it! Chances are the monthly pet is only going to become uncommon, rare at the highest, and will be much easier to trade for after the demand has died down and the rarities have been shown.
3. Adopt as many pets as you can from free adoption centers, even if you don't need them. Through adoption centers you should be able to find tons of pets to help with your collection. If you adopt pets you don't need, add them to your duplicate group(s) for trading later!
4. Make sure to participate in every event! You should try to collect as many tokens as possible during events, and try to obtain every event pet. Even if you end up with duplicates, keep them for trading. During events, many users will overpay for event pets and/or tokens. Usually, the overpay is a good deal. Event pets usually become much easier to tarde for after the event ends, the demand dies out, and the rarities are shown, so don't worry if you don't collect all the pets or end up trading some for overpay!
5. Trade your duplicates for pets you don't already have. There are tons of users on the trade forums that would be willing to trade.
6. Make sure to log on every December 18th for the chance to get some of the rarest pets on CS! Users often tend to overpay for the baby versions of their most beloved pets so it can be much easier to get overpay for some of them.
7. Check often to see if the pound has an opening. The pound has many pets that need homes and chances are you can find a pet you need for your collection; if you get lucky maybe a rare or above!
8. If possible, buy every store pet set. This way, you won't fall behind on your store pet collection. Remember, store pets are never re-released so if you're trying to collect every single pet, the store pets are a good place to start. If possible, buy extras of the store pets sets so you can keep them in your duplicate group(s) for trading later on.
9. If possible, open an art shop! This is a great way to gain valuable pets in exchange for your art.
10. If possible, participate in art competitions. If art isn't your thing, there are also writing competitions on the art competition board from time to time. Usually, valuable pets are offered as prizes.
11. If possible, join another website to acquire currency to trade. Many users will accept other site currencies or items in exchange for CS pets, items, or C$.
I hope these tips helped you out a little bit as they're the ones I follow to help me with the same goal and they've been helping me so far!