Just installed a new toilet and it does perfectly until we put the lid of the tank on, then it leaks at the base.

Leaks all the time or only when flushed? All the time is likely the two brassmounting bolts. Use no caulk but double check the instructions to make sure you have the several washers in the right squence. Tighten until there is aonly a very slight wobble or wiggle between the tank and the toilet