I live in San Diego, and it would not occur to me to take anything more than my drivers license to TJ.
As for transport, it's very easy to drive to the border and park in a lot on the US side, or take the trolley to the border. Walk across and take a bus for about $1 to Avenida Revolucion - or take a taxi, as Stimpy has recommended.
If you want to drive into Mexico, and you are taking your own car, be sure to buy Mexican insurance as soon as you cross the border. US insurance does NOT cover you. If you want to drive a rental car, be sure that the rental company alloows you to take it into Mexico. It's a pretty drive on the free road thru Rosarito along the water down to Ensenada.