The Bible (old or new) doesn’t say much about which sin is worst, but it is safe to assume Pride is high on the list, because of it’s flexibility and volatility when in excess. This makes sense in more than just a religious context.
It should be noted that these sins often lean on each other and form a complicated “chain effect” with the excess of one leading to the excess of another. That said, Pride (arrogance, really) is a fundamentally “bad” sin to overindulge in.
Think about it — what is one thing every tyrannical ruler, every classical supervillain, every corrupt leader or even cult leader has ever had in common? They were all vain, generally arrogant people. (for the sake of not offending people, I won’t drag God into this). And what happens when you become so arrogant that you become egocentric? You become selfish. (Avarice/greed). Greed inherently begets Envy, because humans are human and like to have what others have just because we don’t have it. Envy can very easily beget Wrath when combined with impatience.
Greed and Pride both can also independently beget Sloth, since having everything or thinking you have everything can make it seem like you have nothing to do. Pride can absolutely beget Lust, what with the potential for feelings of entitlement. Greed, too, can beget Lust, as can envy. Even Sloth can beget Lust, because of boredom.
As far as inciting the most volatile chain-reaction, Pride is the worst.
As far as how many other sins can be linked to it, Lust is the worst, for there is literally not a single other sin that can’t beget Lust in one way, or which Lust does not beget itself. Wrath can beget Lust, and Lust can certainly beget Wrath. Hell, even Gluttony can beget Lust, for the gluttonous are often also greedy and can “hunger” for more than just material food.
As far as being the worst or most damaging unto itself, Wrath is the worst. Being perpetually angry hurts you and everyone else, and ultimately leads to all kinds of wrong-doing.
So among them, Wrath, Lust, and Pride are probably the worst.
For those who aren’t familiar with them, the seven deadly sins, in Christianity, are pride, envy, anger, sloth (laziness), gluttony, lust, and greed. The idea is that each of these sins leads to greater sins.
I don’t believe they have ever been ranked in terms of ‘badness’ (please correct me if I’m wrong); however, pride is at the root of all (or most) other sins. The very first sin, Adam and Eve eating the forbidden fruit in the Garden of Eden, was triggered by pride: they wanted to be like God. If you dig back far enough, you will find pride at the root of nearly any sin.