Big Jim once said that one of the first rules of troubleshooting is to take care of issues that you know of first.
However, if you want to do the P0171 first, then, spray some carb cleaner to try and locate a vacuum leak. If the idle changes you found the leak. There is a very good chance that the P0171 is the result of a vacuum leak.
As for the P0420, as posted earlier, take care of the P0117 (ECT sensor) first and see if that will also take care of the P0420.
