Twenty years ago, humans were the only race on Talothian, though they were as varied as people in our modern world. The invasion brought elves and dwarves, but by and large they are not sympathetic allies (and thus not good PC races).
Elves are so few in number that any pure elven character living in Lasthold would be the only one, and he or she must be an outcast from elven civilization, probably be mistrusted by humans, and likely be some kind of servant (or captive) of the city. The dwarves are greater in number but their hive mind makes them unlikely to revolt against their race. One group of dwarves, the Unbidden, have broken away from the hive mind and live in an underground complex a few days from Lasthold; they are the only likely origin for dwarven PCs.
When people of different races create children together, the people of Talothian call them “hybrids” (yes, it’s racist). A lot of the hybrids or “half” races with an elven parent are the product of slavery.
Half-elves are what humans call a mix of elven and human blood.
Gnomes are what they call a mix of elven and dwarven blood.
Halflings are what they call a mix of dwarven and human blood, but this is a rare pairing these days (since dwarves find slavery abhorrent).
The other races in the Player’s Handbook are too rare to consider as regular player characters.
Mechanica are the Talothian equivalent of warforged, and are valid choice for player characters. Any mechanica living amongst humans would be treated with suspicion and sometimes treated as a nonliving creature.
As there are no intelligent dragons on Talothian, there are no Dragonborn.