You can pick anyone, or randomly choose one. Your patron troll luckily has lots of artwork so if you want a good Terezi picture it isn't as hard as one for Equius. Terezi is just one of the more popular trolls XD
Really, i don't know. JUST PICK THE ONE YOU LIKE MOST or pick one of the ancestors. My avatar is the Handmaid, for example. But there are many others who don't get a lot of love, like E%ecutor Darkleer or Orphaner Dualscar :P