Getting from Emeryville, CA to Mountain View, CA with significant luggage

BART does not have luggage areas/racks as such, however all cars do have a large open area intended for bicycles and wheelchairs. Depending on how busy the train it at the time you get on you may be able to get the seat directly next to this area which will allow you to sit down and still control your luggage, or you may need to stand if that seat is taken (or if it's needed by someone elderly/disabled).

Your biggest problem with taking BART is that there's no BART station at Emeryville! There is a free shuttle to the MacArthur BART, which introduces even more issues with your luggage! Your better option would be to get off the Zepher at Richmond station, which allows for an easy change to BART.

Getting from BART to Mountain View involves changing to Caltrain (and buying a new ticket) at Millbrae. Caltrain does have luggage racks in the 3rd car from the BACK of the train on southbound trains.

At the time you're talking, both BART and Caltrain will be relatively busy. For the first part of the BART ride you'll be headed into the city so it shouldn't be too busy, but expect it to full up once you get to the city stops.

The other option would be to use something like SuperShuttle - either for the whole trip (you'd probably go via SFO and change shuttles there) or catch BART to SFO airport and go Supershuttle from there. It'll cost more, and probably take longer (especially during peak traffic), but will have the advantage of dropping you directly at your destination rather than at the Caltrain station.

Haven't taken the Capitol Corridor yet, but I know for sure that CalTrain is a valid option. BART doesn't have any designated luggage spaces, but you can take your luggage on it. BART goes to SFO and OAK after all, people do it all the time.

You can take BART, then switch to CalTrain which has a couple of stops in Mountain View, or you can take the Capitol Corridor and then switch to VTA light-rail (that has bike racks, but you can put your luggage there as well, I guess, even though its not as convinient). Switch to light-rail in Santa Clara or to CalTrain (going back to SF direction) in San Jose if you're taking the Capitol Corridor.

I'm fairly certain that at least some cars on the Capitol Corridor have a luggage area by the stairs (I forget if it is upstairs or downstairs). You could ask the conductor as you board. There are also overhead bins for smaller items. The times I've ridden the Capitol Corridor it has never been crowded, but that's never been at 5pm on a weekday.

BART definitely has no luggage areas of any kind, and it's not very convenient to get to BART from Emeryville (you would need to take a bus or taxi). Around 5pm the trains are likely to be crowded, especially during the week. If you do decide to take BART, you should get off the Zephyr in Richmond, where there is an intermodal station and you can transfer directly to BART.