Why Do I only Get Carmen?

During your first few days in the game, you'll most likely earn basic host code as a random drop reward from doing interactions. And though what you get is a basic host code, it most likely that you'll get Carmen when you manufacture it as she tends to have the highest percentage of being drawn out. Although, you might think she is useless other than performing card games, it is good to have lots of basic hosts as you can later on use them when you re-build higher tiered hosts you have.

Be patient as the game does not give away 3-5 star host codes that easily. If this is what you are aiming to have (a better tiered host), what you should do instead is to work on your objectives (the achievement-like system in the game). Usually, when you've successfully cleared and objective, it will reward you with coins, gems, or host codes. The usual case is, when it gives you a host code, it will be at least a 3-star host.