I live in Menlo Park (the stop north of Palo Alto). I have taken Caltrain to and from SFO airport and I have taken taxis.

1. If you arrive at the airport, walk outside and take a taxi from the taxi stand to Palo Alto you will have to pay ~80 to 100$. This is because there is a 15 mile limit on travel from the airport. After you pass this 15 mile limit, the fare = what shows on the meter + 50%. When you head south from the airport towards PA, the 15 mile limit is passed somewhere in Redwood City. I have paid 85$ (with tip) for trips from SFO to MP.

2. If you pre-arrange for a taxi to be waiting for you when you arrive, the trip from SFO to PA will be significantly cheaper. Taxis with whom you make a reservation do not charge the +50% fare top off. I've never actually booked a taxi to come to the airport and meet me, but the phone book lists the following:
International cab 650-365-2004/800-507-7210
Yellow Cab 866-663-8880
VIP taxi 800-737-4VIP

3. Caltrain. When you arrive at the domestic terminal you need to either walk to the international terminal or take a free 'train' to the international terminal. At the international terminal you catch the BART (you have to buy a BART ticket) to Milbrae (about a 5 minute) ride. At Milbrae you get off the BART train, negotiate some escalators/elevators/stairs and buy a ticket for Caltrain. You wait on the Caltrain platform for the next train. The BART ticket will probably cost 1.50 to 3$. The Caltrain ticket will cost $3 to 7$.

The # of stops that the Caltrain makes depends on what train it is. Baby Bullet trains do stop at Milbrae, but not all stop at PA. Non-Baby Bullet Trains sometimes don't stop at Milbrae, some do...it's all complicated.

You can find lots of info at either
www.caltrain.org
OR
www.511.org (an interactive trip planner that will tell you all about the public transportation options).

Hope that helps