Remember, you are from Texas!
Although you guys think the price of petrol is high stateside right now, it is currently around the equivalent of US$ 10.70 a gallon here in Portugal. A small car will use about 3 to 4 gallons for the Lisbon to Lagos run depending on loading. Add the tolls and you are looking at a minimum of about US$ 55.00 if you take the motorway.
Also as you are from the otherside of the pond, remember that most vehicles this side are manual shift. If you need an automatic, remember to specify this when booking and be aware that you will pay a premium for an automatic vehicle.
Train tickets are about € 20.00, not US$ 20.00
You will need a car in the Algarve so better to hire when you arrive the Algarve.
As regards train stations, your best bet is to take a taxi from Lisbon Airport to Gare Oriente Station. (About 5 minute drive.)
From there you can get either a long distance RENEX Coach to Lagos or the train, changing at Tunes.
For direct links to timetables, see my blog at
http://barlaventostravelblog.blogspot.com/
Scroll down on the right hand side panel till you come to:
»» Algarve & Portugal - Travel Transport Links
»» Continue scrolling down in this section till you come
Portuguese Railways - 2008 - Lisbon - Algarve Faro/Lagos Timetable
or
RENEX Bus Service - Lisbon to Algarve timetable
Click on these to download the timetables from the respective sites.
