If you want to rent a car, here you have the sites of the main companies which offer car rental in Madrid. Basically the same service, there is sometimes difference in price:
Long distance parking in Madrid Barajas airport
Madrid goverment mobility page with public parking
Madrid Rings & Highways Network:
Madrid has 7 main highways entering and leaving the city: A-1 to A- 6 and the A-42. The A stands for Autovía (highway), and P stands for Pay (peaje - toll), therefore, the AP -6 is the toll highway 6, while A -6 is a non payment highway. Madrid has three major ring roads, the inner-one known as the M-30 circulates inside the urban centre, and therefore, it often has heavy traffic, the outer ones are the M-40, which stretches round the suburban Madrid and the M -50 which runs across what are still today fields. The radial roads R -which are toll paying roads- link the three ringways (M-30, M-40, M-50), in order to avoid taking the A roads, which are ussually more congested.
There are now 'Deterrent Parking Areas' at some train and metro stations in suburban Madrid, which allow you to leave the car at a free of charge parking area and take public transport to get to the city center.
A-1 (Burgos Highway)
Also known as the 'Autovia del Norte', this highway connects Madrid to Burgos and Santander, to the cities of the Basque regions (Vitoria, Bilbao, San Sebastian), to France via Irún, and to the ferries to the British Isles.
A-2 (Barcelona Highway)
This is a direct highway to Barcelona and the Costa Brava, via Guadalajara, Zaragoza, through the Monegros desert, and Lérida. Also connects to Southern France via Portbou.
A-3 (Valencia Highway)
Used for travelling to and from Cuenca, Albacete, Murcia, and the following Mediterranen cities/costal areas: Alicante (Costa Blanca), Valencia, and Castellon (Costa de Azahar), and an alternative route to eastern Andalucía.
A-4 (Andalucia Highway)
This is the route to and from the following cities: Cuidad Real, Jaén, Cordoba, Sevilla, Granada, Almería, Malaga, Cádiz, Jerez de la Frontera, Tarifa, Costa del Sol, Gibraltar and the ferries to Morocco.
A- 5 (Extremadura Highway)
Highway to Talavera, Trujillo, Cáceres, Mérida, Badajoz, Lisbon and Southern Portugal. Also, an alternative route to western Andalucía.
A- 6 (A Coruña Highway)
Leads to: El Escorial, Segovia, Avila, Salamanca, Valladolid, Zamora, León, the cities of Galicia and Asturias, and northern Portugal.
A-42 (Toledo Highway)