To get the best chance of finding great trades or other players to roleplay with, you're more likely to find someone in a server with the largest number of people. Adopt Me's server capacity is 48 players, so you're bound to find the person you're looking for.
But how do you get into a server with 48 other players? Look no further!
The first step is to head to the Adopt Me game page on Roblox and click on the "Server" section on the lower right bar, or click here to bring it up for you.
Then by scrolling down the page a little, you'll find a section labelled "Other Servers" which brings up a list of all existing servers to join.
By switching your filters to "Number of Players: Descending" and checking the "Exclude Full Servers" box, you're left with a list of almost full servers for you to join. Sometimes if other users are using this same trick, those servers can fill up easily, so its always best to keep refreshing and join quickly just in case.