Help for newbies

Start with hardtails with a suspension fork. Upgrade to better full-sus bikes later, if you like the sport and can afford to do so.
I'd recommend something like a Vitus or a Diamondback; great spec components, not too pricey.

I'm sure you can find something for your Corolla, but I don't have any personal experience with racks. Look at Thule, Kuat and Yakima racks to start, but I'm sure there are lots of other options.

Ditto. I would like to add that some stats you will want to look for are 29" wheels, a Shimano drivetrain (stay away from SRAM SX, cheap crap), and air suspension. 29ers are really the only way to go because 27er or mullet (29" front, 27.5" rear) are for flickalbility and playing on jumps, not efficiency and the ability to roll over obstacles. Shimano's components are amazingly consistent in operation. I had a Deore 10-speed drivetrain that showed itself to be completely indestructible over five years of use with little matenence. Sram is okay too as long is it isn't SX. You can get an air fork for not that much more than some crappy elastomer SR Suntour fork. Rockshox provides great performance with easy serviceability. The best thing you can do for yourself now is research for a good parts spec.