Zoo Staff
There are 5 types of staff in the shop. All staff get increasingly more expensive depending on the numbers of species you own. A good idea would be to save up for a while and but the desired staff in bulk early. For example, you can buy 10 Kiosk manages at the "0 Kiosk Manager owned" price, instead of buying one kiosk manager, then having the price go up, then buy another one, then having the price go up again, then buying another one, etc..
And if the game tell you you need a staff, buy or recruit one. Because it will affect your daily profits if you're short staffed.
Veterinarian
You only need ONE vet in order to start breeding animals. And it seems it's really all you need. The only exceptions are at certain levels of the game, the achievements calls for you to purchase a certain number of vets for your zoo. Otherwise, they seems to serve no other purpose.
Kiosk Managers
You need one kiosk manager per kiosk stand that you own. So budget that in when you wish to purchase a new kiosk.
Maintenance Manager
You need 1 maintenance manager for every 10 animals, not species, that you own (For example, if you have 20 elephants, you'd need 2 Maintenance Managers).
Breeding Specialist
These cost 80 Wildlife Points each, and only allows you to breed one additional animal at a time. Hardly worth the cost. You DO NOT NEED a breeding specialist in the game.
Treasure Hunter (soon to be removed from the shop)
These also cost 80 Wildlife Points each. She will accompany you when you visit your friend's zoos and seek out the treasures for you. So basically, all you have to do is click into a friend's zoo, and it will automatically give you the treasure from that zoo, no matter how many island the zoo has. Again, you definitely DO NOT NEED a treasure hunter. But if you have a lot of zoo friends with large zoos, this can cut down your treasure hunting time significantly. It's definitely a more worthwhile wildlife Points purchase than the Breeding Expert. In fact, it's probably one of the best use of your Wildlife Points currently in the game.