Shuttle to Caltrain is free: "VTA SJC Airport Flyer (Line 10) takes you between the Santa Clara Caltrain Station and the San Jose International Airport. The Airport Flyer is free and operates seven-days-a-week from about 5:30 a.m. until 11:30 p.m. Buses operate every 15 minutes on weekdays and every 30 minutes on nights and weekends. Avaya Stadium, home to the San Jose Earthquakes, is located between the train station and the airport, so the bus may experience delays when there's a game or event at the stadium."

I don't recall any issues with the large bag I took with me, either getting on or off, or putting it in the racks. Caltrain was fast, nice and simple. I do like trains though. Will take you into AT&T park so will need a taxi from there to hotel, I'm guessing.