Pew has a big new report on that topic, with this summary of the results being a handy guide:
A few things pop out to me here. Like other surveys it shows broad support for background checks on private sales, even among Republicans. It also shows a clear majority for “assault weapons” bans — which, interestingly, didn’t show up in a 2015 New York Times poll. The biggest gaps between Republicans and Democrats, meanwhile, are on questions of expanding where people can legally carry guns. And I’m not sure how to interpret the question about “shortening waiting periods,” because, well, there isn’t a waiting period, at least on the federal level.
Finally, there are two questions where Republicans surprised me. One, they support a “federal database to track gun sales.” Currently, guns are traced through their manufacturers and the stores where they’re sold to avoid placing those records directly in the government’s hands, but it turns out that most Republicans aren’t so concerned about a centralized registry. And two, by more than two-to-one, Republicans oppose permitless concealed carry, which has expanded quite a bit in recent years and is a major goal of the gun-rights lobby.