The starter living ticket/undead ticket is like, basically, when you join EJ, you automatically start off with one living ticket, and one Undead ticket; so that, you know. You can actually make a character and start your adventure into EJ. X"D That's all it means by 'starter tickets'. Just something to get you started on EJ.
As for Infected needing Undead or Living tickets, as Infected are technically still alive, I think they need Living tickets...? Or at least, that's my speculation, man.
EDIT: Okay, I asked a friend. They need Undead tickets. I assume this is so because Infected are generally slated to become Undead later once their pulse stops, and changing out tickets would be tedious, maybe? Or I guess because Undead and Infected are generally around the same tier. lol