Most shelter animals have been bounced around from home to shelter, or feral environment to shelter. Their nerves are ragged, their diet inconsistent, their health-marginal.
I posted a topic here titled "Care and Feeding". It is valuable to anyone welcoming a pet to their home.
To minimize the risk of them either throwing up or having diarrea on the way home

bring Pet Flora with you. Depending on the size of the animal, give them 2-6 capsules and take them for a 10-15 minute walk. This accomplishes two things:
1. This allows them time to adjust to your smells and persona away from the shelter.
2. During this time the abundance of good bacteria Pet Flora provides will have time to calm their GI tract.