To unlock A Complete Set trophy in Assassin's Creed III Remastered, you will need to see all of the different optional characters settled at the Homestead. The earliest you can unlock this trophy is during Sequence 9.
Characters that you can recruit for your homestead will be displayed on the map with the "Homestead Mission" icon. If one of the characters isn't showing for you, concentrate on recruiting the ones that are available, as some will require another character to be recruited before their mission will be available.
You can view the different character, their initial location and when they become available below (credit to A Flash Bangado for his guide on TA):
Farmers (Warren and Prudence): Becomes available during Sequence 5, can be found in the Eastern section of Monmouth in the Frontier.
Woodworker (Lance): Becomes available during Sequence 5, and can be found in the southern area of the Homestead.
Huntress (Myriam): Becomes available during Sequence 6, can be found in the Northern part of the Homestead.
Miner (Noris): Becomes available during Sequence 6, can be found somewhere in Boston, can't remember exactly where.
Innkeepers (Corrine and Oliver): Becomes available in Sequence 7, can be found in the central part of the homestead. However, I think you need to have completed a fair amount of homestead missions beforehand to unlock this one. This mission is paramount to unlocking the missions for the other characters.
Doctor (Lyle White): Becomes available during Sequence 7, can be found somewhere in Boston.
Blacksmith (Dave): Becomes available during Sequence 8, can be found in the Frontier near the exit to the Homestead.
Priest (Timothy): Becomes available during Sequence 9, can be found in the central part of the homestead.
Tailor (Ellen): Becomes available during Sequence 9, can be found in New York.
NOTE: The characters I haven't mentioned here are the Lumberjacks (Godfrey and Terry) and Achilles. Both of these characters settle into the Homestead as part of the storyline and are unmissable.