Depends on your mode. Sandbox, you're pretty much limitless.
Career and scenarios, you have set goals (scenarios are timed)
Challenge and franchise are very similar. Challenge, you run 1 zoo offline. Franchise, you can have multiple zoos and even trade out animals between them but needs an internet connection.
If you're playing in franchise and/or challenge, I'd suggest you start off with 1 or 2 vivariums for quick cash. Ideal would be the poison frogs or red-eyed tree frogs, as they breed fast, and you can sell the offspring for a fair amount of cash (just remember to keep at least 1 breeding pair). Don't forget to have a drink stand and a food stand, 2 or 3 vendors and a keeper.
Once you get enough cash, get a good starter animal. DON'T SPEND TOO MUCH OR ANY
CONSERVATION CREDITS (CC). These are important to get rarer and more popular species. You gotta build up by breeding and releasing into the wild other animals.
Good starting animals:
- Warthogs
- Red ruffed lemurs - 1 male and multiple females can give a lot, as they can have up to 3 offspring and each one can be released for 45 CCs. I'd suggest, with lemurs, you keep any female offspring and release the males. Then, replace your breeding male with new blood to prevent inbreeding. Keep repeating this and you should get enough for an upgrade soon
- Nile monitors
- Some people suggest cheetahs