Well, I don't have possums, though do have the odd rabbit come visiting from the open land accross the way, they do eat the occasional seedling (small flowers bought in punnets) off. Not really sure how you'd go with possums, aren't they more fruit eaters?
If you want to start off small, go for the pots, but get nice large ones, maybe a planter box - I have an old cement laundry tub that makes a great garden bed for herbs, just make sure that you ensure you have good drainage holes in the bottom of what ever you decide on. Then make sure you have a good quality potting mix, perhaps one with water retaining granuals or mix some of these in, especially if you are in a dry area - you will get bitter and woody herbs if you don't water them enough. I don't think you should have an issue with cats - do you have a dog?
As for covering, it will depend on what you grow and if you get frost in your area - ask the nursery person what is frost hardy adn what isn't, they will always be willing to help out.
Also make sure they are in plenty of sun for nice strong growth and you will need to fertliise a couple of times a year.

Lots to learn, but have fun!!