I think in general we need:
1. An african arboreal monkey (my choice of course is the black and white colobus monkey)
2. A savannah primate (my prefered choice would be the vervet or patas monkey but the olive baboon is also an option)
3. An Indian primate (lion tailed macaque being my preference, but the hanuman langur is also iconic)
4. South american primates: howler and spider monkeys, golden lion tamarin and squirrel monkey. Of course that something like saki or uakaris would be cool but i think those four are essential to complete the latin american primate roster.
5. Baboons: the ones missing are the hamadryas baboon (which will give representation to the Middle East) and the Geleda baboon (which i prefer over the other mostly because of its unique biome and behaviour). But having both is also good in my list, i just think that i prefer more tropical primates over baboons and with just one i'll be fine
6. Golden snub nosed monkey (just cause i really like them, they are in my top 5 primates i want for the game and is a monkey with a particular biome as well, which would give more variety)
7. Lemurs: i think the sifaka and the aye-aye are the ones missing
8. Gibbons: i don't think is essential to get another gibbon but a lar or white cheecked gibbon would be welcome (just not yet, maybe give the spotlight to other primates that need it more first)
9. Nocturnal primates: loris, tarsiers and galagos basically (my choice would be a loris, but a creepy tarsier is also interesting although they are maybe to small for working as a habitat animal)
Then there are a bunch of primates would be cool to have just because of their striking appearence like the red-shanked douc, the golden langur, the red colobus monkey, de brazza's monkey, the emperor tamarin, the francois langur, bald uakari, white faced saki, mouse lemurs... but they are not priorities.