I think your idea of picking up the car at Lisbon Airport is a good one. You have good access to the A2 motorway to the Algarve via the Vasco da Gama bridge close to the Airport.
As regards taxis, they are metered. However, there is an excellent bus service from Lisbon Airport to the Avda. Liberdade/Restauradores/Rossio area operated by Carris.
See: http://bit.ly/9b2Ga3
A taxi for 4 people & bags may be difficult. Hopefully there will be a slightly large people carrier on the rank. With bags, and dependent on time of day/night/weekend budget between € 10 and € 20 per run.
I am totally confused by this obsession with GPS. My main profession is as an IT Tech and web designer of some 15 years experience. I like Technology.
Yet I cannot fathom this fascination with GPS, when MK 1 eyeball, a good (Google/Michelin) map and an adventurous spirit will usually quite adequately get one where one wants to go.
BTW as you are from the "other side of the pond", remember when booking your car that most rental vehicles in Europe are "manual shift"! If you want/need an automatic shift, remember to specific this when booking and be aware that you will pay a premium for such a vehicle.
