The game will tell you that you need all of the Staff facilities, but you will quickly run out of money that way.
You will want a Trade Center, Staff Building, Quarantine, and Keeper Hut at first. You shouldn’t have to have a Vet Surgery just yet, because animals usually get injured when fighting rivals and you aren’t going to have many animals just yet.
Research and Workshop are useful, and you may want to dive into researching immediately, but I find it is better to wait until you start earning money before building these, since they do not generate money themselves.
For Guests, a Merchandise shop will help bring in money, and eventually Food / Drink and toilets. But you dont’ need the Food / Drink or Toilets just yet, you can wait until you start getting some money coming in.