This is my first breeding project and I would really appreciate help and advice from those who are more experienced.

What methods do people use to keep track of which pets are related and have what genes? Currently I'm using the names to keep track of traits but I have no quick way of figuring out lineage other than through the pet's tab.

In terms of genes I tend to only list what they have e.g. G1c G3c instead of listing G1c G2 G3c M1 M2 M3 because it tends to make it easier to spot high tp pets and to easily identify the genes.

In terms of family trees I label my ones by generation and give each project a code.
So if my project name is Night Sky then all I the pets for that project have NS in their name, which also helps you to find them in advanced search to weed out the bad ones once you start building them up.

The first generated pets just have their genes listed but I then call their offspring NS (then their genes). The offspring of this generation are then called NS2, and the offspring of that generation are called NS3. So I now know that any pets with the same generation code will not be able to breed. I also know that any females are able to breed with males from one generation up.
I hop that helped and you can have a look in my projects tab to see the layout and generations if that might help ^-^