Well since the whole thing is a thought exercise, let’s do the thought exercise from an economic standpoint.
I’d argue that the only two states — or at least the best states — that could actually make a go of it economically, would be ideological, economic, and political foes Texas and California. Arguably, those are the primary states that have it all and could get out.
both have a long shoreline and a direct border with an important trading partner.
Both have oil and natural gas production capacity.
California has three great seaports (LA, LB, and Oakland for those who are unfamiliar), Texas has one of the greatest seaports in the world (Houston).
Both (were they politically inclined to do so) could become net energy exporters. (although Texas probably could become one of the greatest energy exporters in history)
Both have high tech in high quantities (although California has higher quality).
Both would have (upon secession) major military facilities to create their own military. One has a spaceport. One is a the present nation’s top agricultural producer, although Texas could become a farm powerhouse as well.
Pennsylvania, with its seacoast and close access to customers such as former fellow states NY and Florida, could also be a force to reckon with since it has a lot of oil and natural gas and rich sites for farming.
I’m sure there are others that might easily survive, but California and Texas would be the best candidates to be successful breakaway republics. (or in the case of California, a socialist republic. California, aka the CSSR - California Soviet Socialist Republic)
I would expect that Texas would not be alone. I think Louisiana, Arkansas, Missouri, Oklahoma, Possibly Kansas and New Mexico would join with it.
It might even reestablish the old confederacy with numerous additional states.
In discussions on the civil war, I have long held the view that if left alone, the original CSA would have eventually looked like this:
