@zach-lipton has a pretty concise answer about airports.
Due to the SFO class B airspace, the training area is primarily NE (Calaveras) to SE ("UTC" / Anderson Lake) of KRHV (and South to East of KLVK). If you're departing from KPAO, it's a good 15-20 mins each way to and from the training area. KPAO also has IMC more frequently than KRHV, which is a big advantage if you're mostly going to fly VFR. It's also further out to get to non-towered airports from KPAO (E16/KTCY/C83 are the closest). Highway 101 N/S is pretty busy around KPAO (Embarcadero exit), so unless you will generally avoid the morning/evening commute, KRHV may be easier to get to by road than KPAO.
KSJC is a busy airport, but they do accommodate GA training operations if they can. I would recommend against using KSJC GA as your transit point though -- KRHV is about 5 miles away, and much cheaper.
If you're a visiting pilot and want to use the transient parking, transient tiedown fees apply -- see KPAO, KRHV. Some FBOs or flight schools may offer lower tiedowns in their ramp areas at the airports.