Like others have said, all factors are equally important, they all need to come together as without one of them, you're still going nowhere fast. They also need to be balanced, as
@allsupratt spoke about. The only thing I think you could do is list the order in which one you need first, but not which is most important.
Initially you need grip to get going. The bigger, softer and lower pressure the tire, the more grip it will provide. The tire needs to be able to put down the power to the tarmac that the engine is putting out. If it can't, it will start slipping, i.e wheelspin.
Weight plays a factor from the get go as well. No good having lots of power and a streamlined car in a drag race if it is extremely heavy. The less it weighs, the better.
Then you need power to get the car accelerating. You need enough to go fast and fight the friction at high speeds, but you need tires that can handle all of that power.
(Aside from obvious factors such as engine size making a difference to power output, the type of fuel that engine relies on makes a difference too. Different classes of drag car use different types of fuel, such as Methanol and NitroMethane. Far as I remember, NitroMethane does not actually "burn", you can throw a flaming rag on it and nothing will happen. It is compression that causes it to explode violently, and it shares an ingredient with TNT. Also, if you've never stood near a top fuel car, if you ever do, you'll essentially experience having tear gas sprayed in your eyes)
Last in the list of what works is aerodynamics. They don't really do much at low speeds, but for high speeds you
need downforce to keep the car planted to the ground, yet also keep it aero efficient/streamlined to reduce drag. Without downforce, the air pushing against the car will cause it to take off.
If you've never been (or anyone else here) to watch drag racing in the flesh, I highly recommend it, it's quite an experience and you'll never forget it. Stand as close to the start as possible to be shaken like no nightclub or concert could ever come close to, and be left with the intense smells of burning rubber and exotic fuels as you see a car accelerate from 0-100mph in just
three quarters of a second. Then take a trip to the finish line to see what 330mph looks like up close and the unique sound one of these monsters making it's way up the track. It almost sounds like the air is being ripped apart and you can both see and feel a shockwave coming.
I always find that when I'm at a drag event and they have F1, NASCAR, WEC etc on some spectator screens, they just feel so puny and slow to look at and listen to. I mean, any one of those cars could zip by a standing top fueller at full speed, and it would only take it
3 seconds to get going from nothing and re-overtake the car that blew by it at 220mph.
Or for another perspective; 2 TF cars racing each other have more power than the entire F1 grid combined.
Edit: Just remembered on old video, the figures are a little outdated (e.g 8000hp then, +11000hp now), but may be you might find it useful.