It's a shame that all those Warm Springs signs went up a month or so ago and will have to be replaced shortly. I think when the new train cars come the lines will be referred to by color rather than destination, which will fix that problem.
The maximum one-way fare on BART is ~$15 and that's if you're going between OAK and SFO (which I imagine is very uncommon). Non-airport rides max out at under $8
If this is interesting to you, you should definitely check out the Bay Model (https://en.wikipedia.org/wiki/U.S._Army_Corps_of_Engineers_B...). Its a scale model of the SF Bay and the Delta in Sausalito that was built by the Army Corps of Engineers. Its admission free!