To make a chess tournament attractive to many people entering (as an alternative to segregating by class or rating), do things that increase variance -- increase the probability that a low-rated player can win or do well in the tournament. Single games of blitz has higher variance. Single-elimination tournaments have high variance. Chess has draws, so not exactly suited for single-elimination; perhaps Swiss permitting repeated encounters until a decisive result occurs. Tournaments with only a small number of rounds have high variance.
Inspired by poker and bridge, which have variance built into the game by being a game of incomplete information.
No matter what the structure, monetary prizes have to be carefully structured, or else there will be incentives for people to pay people off to throw games. Every game must be zero-sum in terms of prizes or expected prizes (though this will induce many draws due to risk averseness). For a single large grand prize, those still in contention for the grand prize must only play each other: there might be some byes due to draws causing an odd number of people to be in the money.