I'd require a signature count equal to 5% of the affected population before a policy can come up for debate.
This allows anyone with a good idea to market and garner support for their idea prior to subjecting it to a vote. If they have a very hard time getting anyone to sign the initial petition, they can refine it until it's acceptable, or they'll eventually give up. If it's a good idea, and has a shot at being made law, 5% shouldn't be a hard number to come up with.
Once it makes the initial cut, a waiting period to publicize the proposal is put in effect. I'd think no more than a month. This allows the people to debate the law, without waiting a ridiculous amount of time to where people simply forget that it was even on the ballot.
After the waiting period, the vote is held in which an affirmative Quorum of the affected population has to be reached in order for the law to be passed. 161
If it fails, it has to start the process entirely over again.
By requiring some leg work ahead of time, it prevents the population from being inundated with having to vote on every crackpot idea, but prevents law making from being out of the hands of the common person. IMO only letting lawyers write laws is why our legal system in the US is so convoluted.
By requiring a Quorum to pass the vote, it prevents special interests from simply buying 5k signatures and then keeping a vote quiet to prevent naysayers from voting. With a Quorum, even if they buy off the initial signatures, they still have to convince a real majority of the population to approve of their idea, not just a majority of the ones that show up to the polls.
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This kind of "keep the vote quiet so only people who we like show up" is a common tactic in the state I grew up in. They passed taxes for raises for certain government workers by only telling the government workers that would get the raise that the vote was even happening. One such election had a little over 100 voters turn out to pass a tax that was levied against 60k+ people. 161