I am sure you will love TS3! I suggest you don't allow aging and definitely don't start a family too soon or you will be overwhelmed. I probably wouldn't even have given her a cat to start with but the company will be good for her :)
I am sure I read somewhere on the forum that your sim can take a pet to uni but I don't remember the details. @igazor should be able to answer that question for you.
I remember when I started out I played a single sim without aging for a little while just to get my bearings. Working on skills and socializing were about all I could manage back then. These days I love big families but it's probably not a good place to start.
Whatever you do, good luck and have fun! One thing I do suggest is using "save as" frequently. Just add a number at the end of the save name or something that will help you identify where you're at. This way, if anything goes wrong or not to your liking, you can just quit and reload where you want.