Using VTA to SJC is very easy. You simply take the light rail to the Metro/Airport station, then transfer to a shuttle bus that will take you to both terminals. The light rail drops you off on an island in the middle of the road. The airport shuttle waits on the southbound side of the street (the side with the tall office buildings and the VTA shelter). The airport shuttle runs every ten minutes on weekdays, every fifteen minutes on weekends, and takes no more than ten minutes to get from the light rail to the terminal.

The lots with available long-term Airport parking are Almaden, Blossom Hill, Branham, Capitol, Cottle, Curtner, Evelyn, Ohlone/Chynoweth, Santa Theresa, Snell, and Tamien. I don't have any information about which lots are safer, but I know that the Tamien station shares its parking lot with a child-care center. It appears to be pretty safe. Apparently, the Long-Term airport parking slots are specifically marked (though I have never seen them, personally). You may want to avoid the Almaden and Evelyn lots since they would require you to transfer from one light rail line to another to get to the airport. Generally, San Jose is one of the safer large cities in the US.

For more information, check out the VTA website at http://www.vta.org