In Diablo 3 for the PC, you can’t just jump to the hardest difficulty right out of the gate, since the game is more level and equipment based than the previous games.
In order to change the difficulty level, you first need to unlock each difficulty. The only difficulty unlocked by default is the Normal difficulty, and you’ll need to play through Normal and beat all Acts, plus get to level 30 in order to unlock and proceed to Nightmare difficulty.
Once you unlock the next difficulty, go to the character selection screen and click the Change Quest button on the left. You’ll see the difficulty option at the bottom, and you should now be able to select the next difficulty and start from the beginning.