To find the level select on the title screen, simply press Up to reveal "SOUND TEST" and press Start. This works because the RAM variable that unlocks the level select is preserved when you reset the console ( Sonic 3 was built upon the Sonic 2 source code, and thus shares a number of RAM variables). If you are playing on a real Mega Drive/Genesis console and don't mind risking the long-term health of your console and cartridges, then another method is to load up Sonic 2, unlock its level select (19, 65, 09, 17 in the sound test), swap the cartridge with Sonic 3 without turning the power off, and then press Reset.
Sonic the Hedgehog 3 is the third game in the 16-bit Sonic trilogy and the first game with the easily-tricked-by-Eggman redheaded echidna, Knuckles. This game has unused playable characters.