The love and loyalty of an animal is indeed a gift. But, I do not recommend trying to become a pet mom until you have looked into it quite seriously.
There is a lot more to having a pet than you might think. It is a very big responsibility. It can get expensive. You yourself may be allergic to animal fur.
You might want to volunteer at a local animal rescue and see how that goes.
In my personal experience, one can certainly have both cats and dogs in the same household provided you take the time to get them used to one another.