The airport is right at the corner of 101 and 880, so you could go either way...

101 is more of a direct route, but is also more prone to traffic, because it pretty much goes right through the middle of all the big cities along the peninsula. 280 is a little bit longer, but everyone always hauls ass on that freeway, cause it's out of the way, and never has much traffic. It's also more of a scenic route, and you get to drive past the Stanford linear accelerator, if you're into that sort of thing.

So, take your pick. If you do want to take 280 the whole way, just take 880 to 280, since you're going to be right there anyway.

So that would be 880 South, towards Santa Cruz, and then 280 North, towards San Francisco.

Should be no problem either way, really.