Are there numerous Thruways?
It seems the first stop would be the Ferry Building!
(I've never taken them from EMY.)
There is a single bus that makes 3 or 4 stops -- Ferry Building is first, then Fisherman's Wharf, then Market Street up around Union Square. (There might be another sotp that I've forgotten.)
Transferring to the bus from the train is easy as can be -- just walk thru the station and the bus is waiting right there. The only problem I have ever had with the bus is that the CZ arrives in Emeryville at rush hour and the Bay Bridge (both east and west bound) can be an absolute parking lot on weekedays. (The traffic on weekends isn't too bad.) I'm planning a CZ trip from Denver to San Francisco in June and I don't think I will risk taking the bus into San Francisco because of the traffic delays -- I'll either take a taxi from the EMY Amtrak station to the nearest Bart station, or get off in Richmond and take Bart from there.
There's a shuttle bus that runs from the station to the nearest BART Station (Ashby, I think). The stop is across the street. The service is run by AC Transit, I believe.
Nevertheless, I think transferring at Richmond makes more sense. I did it on from the CZ in November, when the engineer had to bed reminded by the conductor to stop because it was the first week for Richmond! If the sleepers hadn't been in the rear, I fear the cars would have overshot the station, the engineer had to stop so quickly!