If I were in your situation, and I had access to a car at will, my ordering of options would be
1. Caltrain baby bullet (about 1 hour from downtown SJ (Diridon station) to downtown SF (4th and King)); both termini are well-served by public transportation. Lots of people do this, and you will see many of the same people frequently. If you want to go straight from SJC to Caltrain, there is a free shuttle (VTA Route 10) from SJC to the Santa Clara Caltrain station, and back. But I am not sure the baby bullet stops at Santa Clara, so you should probably go online to check the Caltrain schedule.
2. Drive 280 (or US-101 to CA-85 to I-280), but beware of potential backups around Sand Hill Road, the I-280/I-380 interchange, and the I-280/19th Ave interchange just as you enter the SF city limits. 280 is a beautiful drive, and good for the soul.
3. Do #2, but park at the Millbrae BART station (near SFO), and take BART the rest of the way. Probably best done only occasionally.
4. Take US-101. Last resort. Terrible traffic, massive delays if there is an accident.