From the airport it's veyr easy for a taxi - there's a line of taxis and as others have said, of one taxi doesn't want you the next one will.

(in town, on the other hand, if I need a cab with one of my cats, I always tell dispatch I have a cat in case someone is allergic or doesn't want to carry pets)

As for renting a car, will you need a car on Sunday itself? If you wait till Monday when the neighborhood Hertz's( called HLE's on the web site) are open you may be able to get a neighborhood deal using code FIFTY or LOCAL as the discount code. I have found renting the cars form a hotel location is ALWAYS more expensive and they don't have as many choices.

If you want to rent a car from the airport there is the Airtrain to the rental car facility (all the rental car co's are under one roof) which is quite easy. Again, it's more expensive to rent at the airport and drop off in town.

More questions - ask away!
And welcome to SF!