There are no tricks you can perform at the "press start" screen. The only tricks I remember were:
-Stage 1-1: you can disappear of the screen if you take the speed shoes and the invincibility and you run VERY fast.
-Stage 1-2: Well, it was a bug. I walked trough a wall (not the wall with the 1-up) and completed the stage without having to touch the water. It's so cold! You can go to the bonus stage if you complete it with 98 rings -you can't grab 100. When I was a child I had a lot of free time, so here is a "trick" that sometimes worked for me: if you have A LOT of rings (99 is a good number) and you press down when you touch the spinning checkpoint, you'll probably enter a bonus stage. But... sorry, no tricks for that part of the game.