I think most people know how probable the first pet you get,
is obtained in the tutorial. I believe that it is the same type, as your starter pet.
I think it would be nice, if if matched your starter, but as a male!
If this happens, then I am sorry to have missed out, but for first timers
it would be cool to have your own project, with your starter!!
- Pepper
NOTE:
for all my ideas, remember that I don't know how much work they would take, they are just ideas!
Thanks!!!!!!!! :D

I don't think many players have a concept of what a "pet project" is. Some players don't even pick all 4 genotype points on their starter.

The scripted capture pet is already the opposite gender of the same species of your starter.
The only things that differ are the color and possible traits it can have.

I've seen the second pet vary from 0vis, to 1carry, to even 2vis for some players.

The wildcard of them being randomized is more realistic imo. You can't expect all the pets in the wild to suit your needs. The fact that you have two breedable pets at the beginning to serve as an unsaid-tutorial to breeding is enough for me.

Once the player has gotten past all the storyline, they should be capable of making enough gold (the ability to make gold is partly essential to support a project) for themselves to not only expand their stable (space needed for a project) and feed all their pets (needed in general).