What was the first jet-powered supersonic aircraft?
One ME-262 Pilot claims to have exceeded Mach 1 in a dive, but the conditions are disputed due to compressibility and later tests that find the aircraft uncontrollable above Mach .84. The first U.S. fighter plane to exceed Mach 1 in level flight is the F-100 Super Sabre. 

For research on how the sound barrier was broken as it results to aircraft design is to read Wikipedia: Sound Barrier.

Wikipedia also has a good read on Supersonic Aircraft that lists aircraft by manufacture date.

As for technological innovations, I would suggest reading about the turbofan engine, specifically inlet design since the air must be slowed sub-sonic before entering the compressor stages.