There isn't any "start" here. There isn't going to be any additional legislation expanding on this legislation.What did you expect to happen? What would have been a "start" to you?
The Democrats got nothing that Republicans would not have already agreed to. A start would be for Democrats to pass and campaign on universal background checks and a ban on assault/automatic weapons--measures supported by large majorities of the population.
Make the Republicans pay for their intransigence on this issue, there probably isn't any meaningful legislation that can pass in the Congress right now, so use it as a campaign issue to force real change.