@SmerdCombos are the main key to getting high ranks, and if an enemy hits you in the middle of one, it breaking means you lose all the points you would've gotten had it resolved. It's best to chain together a lot of enemies without getting hit, or at least via letting the combo resolve itself if you feel like it may be broken soon. Very risky, but that's the game!
The color of the combo text (starting from orange and yellow, then moving through green and blue and eventually pink and red for the highest tiers) determines how big the bonus is when the combo ends naturally. Try to shoot for the higher tiers for lots of points! Not only will you get way more points than if you'd been slapped in the middle of it, but you may unlock an extra life in the process by getting your score high enough, meaning more points for the remaining lives at the end of the stage.
Keep in mind that combo points are actually based on damage done, not number of hits. So hitting a Donovan 10 times to beat him is worth the same amount of points as just kicking him once into a pit for an instant KO.
The Stars can help get you out of a jam or get a combo to keep going when things look tough, and depending on the situation, that can often be worth more than the 500 points you get at the end of the stage for the remaining stars.
@GuillaumeYeah, Floyd does a good job at linking together disparate sections of a stage. That said, I'm terrible with him for whatever reason! I tend to like Axel and Blaze, as both of their blitzes can hit enemies off the ground for more damage. But one's mileage may vary (those two vets are among the slower characters).