Support for democracy itself is at the top of my list. This includes 1) abiding by the outcomes of elections and 2) a willingness and ability to do the kind of political negotiation and compromise that's necessary to get things done in a multi-party government.
From your list, I checked civil rights and immigration. I'd add addressing climate change (and caring for the environment in general) to the list.
At the state level, I'd add proper financial support for public education, but that's more a state issue than a national issue, so the president doesn't really have to be a part of that discussion.