Crazy traffic at base

So, I was told in my pre flight briefing that  there might be chances of me flying a right traffic pattern today (but chances are left traffic are accounted more). After the briefing, I did become a bit nervous, since Class C airspace could get quite crowded at times, and my reaction time towards ATC instructions may lag, if it's something new to me.

The busy traffic started once I tookoff from the runway. My first initial contact to tower to fly a closed left traffic pattern was diverted to flying a right traffic pattern, because there were helicopters around the left traffic. There was no time to complain whether I should extend downwind and whatsoever, I tried outmy first take to the right. On downwind, it was sort of going well, runway looked like it was 3/4 mile from my gas cap. Till I got to the point where I had to turn base, ATC issued a instruction 'continue with Left Traffic pattern', I got a little confused, since I was targeting to land on 29R, and I saw that there was another plane flying on base adjacent to me to land on 29L. It was a good thing my instructor took over controls quickly to bank a steep turn for 29R. And handed over the controls back to me to continue with my glide path. And I still managed to land a safe one. However it was bad decision making on my side when turning base, as I overshot a bit. 

Well second round of the pattetn I made extra sure if ATC wanted me to fly R or L? So as a was told the next pattern ahould be Left traffic. As a rule of thumb, writing the instructions down is helpful for  double confirmation of what you hear. If you are still unsure about the instructions given. Get ATC to confirm again!! Very important to make sure your given instrcutions are read back correct and taking action correctly. 

Well landed nicely on all tries today, just lacking a better response to my situational awareness in a traffic heavy location.