Something to consider- Boats that Sport Chalet charters is probably going to be very heavy with open water students. That limits the dive sites that can be visited. On the other hand, that might be OK for your girlfriend. The Santa Cruz/Anacapa trip is to the northern islands and usually departs from Ventura/Santa Barbara (90-100 miles north of LA) or will leave the night before. Its a several hour trip from LA by boat.
Very few dive shops out here have their own boats anymore. They just charter the established boats when they need them, and the boats are their own charter agency. Dives here are not guided (No DM in the water with you) so you are on your own unless you hire someone, or a local offers to buddy up with you (which happens a lot via Scubaboard).
Some boats offer tanks (which makes the rental issue easier), and yes, they are refilled between dives during the surface interval. Some also offer weights. make sure you know ahead of time what they provide and what they don't.
Finally, consider exposure protection. If you are used to warmer waters, a 7mil by itself may not be enough for you over 3 dives. Temps right now are about 57F, and can get colder. You'll definately want a hood and good gloves. It would be a shame to have o sit out the last dive because you were too cold. That also means wearing a lot more weight than you are used to. Be prepared for that.
All that being said, I am sure you will have a great time out here.