If we're using recent history as a guide, "presidential material" roughly translates into Ivy educated attorneys with non-Coastal roots (both Clintons, the Bushes, Obama, Gore, and Romney all fall into this broad category).
Gideon and Cunningham don't seem to have been educated in a sufficiently "elite" environment to provide them with the socialization necessary to become President (UNC is marginal here, and Cunningham may be able to counteract this with his military background, but UNC is still more of a "Southern good ol' boy law school" than Harvard or Yale). JPK3 is obviously the frontrunner in terms of being "presidential material" (even though he's Coastal, his name is an overwhelming...lightening rod?; "asset" sounds too generous here).
On the Republican side, Cruz, Cotton, Pompeo and DeSantis all fall into this broad categorization but I can't think of any 2020 House/Senate nominees that are jumping-out at me.
Not many people outside of MA care about the Kennedys these days, or at least the family name carries far less cachet with a younger generation of voters who have no memory of the Kennedys being an integral part of American politics (such voters would make up a large chunk of the primary electorate in a future where Joe Kennedy III would run).
