Every time you get a game over, you continue with more and more extra lives. If you want to, you can stock up on extra lives by purposefully getting a few game overs in a row.
When you play as Sonic & Tails, stand next to Tails (wait for the arrow to appear) and jump to have Tails pick you up. Alternatively, just play as Tails and skip over most of the levels.
I find the game is much more fun on replays than your first play, as you don't have to be nearly as cautious anymore.