For general advice on saving money on car hire, read the Simonseeks money-saving guide. For the best rates use a broker, or price comparison website, or use the Kayak booking tool above.
Most of the big operators, such as Hertz www.hertz.com, Avis www.avis.com, Europcar www.Europcar.com, National Atesa, Auriga Crown www.aurigacrown.com, Sixt www.sixt.es (my personal favourite) and Pepecar have offices at the airport and/or Santa Justa railway station.
You really don't need a car to get around in the old centre, as almost everywhere you will want to go is within walking distance. In fact, it's best to avoid using a car, as a lot of the streets are pedestrian or for residents only, and the one-way systems are a nightmare to navigate. Parking is a perrennial problem, both expensive and difficult to find, and although most hotels have parking, its not always on site, and is usually expensive.
You must be over 21 to hire a car, and to have held a licence for at least a year. You also have to provide your credit card details as a guarentee, even if you pay by another method. And if you wear glasses you are required to have a spare pair with you.