Navigating the first screen without unnecessarily slowing down can be tricky, especially because you want as many eggs as possible for 1-8. Fuzzies are randomly generated, so you either need to clear the path in front of you by shooting an egg or two, by spitting one of the rolling enemies into the Fuzzies, or by just praying for good spawns. If you do get fuzzied, jumping as soon as possible after touching the ground decreases the slowdown. Try to avoid landing on upward slopes as they can completely kill your speed.
Spitting the melon bug at the piranha and the two mildes at the end of the room will allow you to avoid all the red coins in the level, saving a half second on the score screen.
Be prepared for this if you decide to spit a Melon Bug (rolling enemy) into the Piranha Plant. Occasionally, the Melon Bug will clip right through the Piranha Plant without actually damaging it. Doing an up-spit from farther left (see video on top right) should consistently kill it.