Private in the libertarian sense. No state involvement. The reasons for this are clear. Civil (state) marriage is more like a feminist bondage contract. You literally pledge that you will support the lifestyle of your wife and give her half of your stuff. And since no fault divorce, every man, who marries now, pledges that he will even do that, when she cheats on your and breaks other obligations in marriage. But as you all know all of the obligations of women have also been abolished.
So what we have left right now is the theoretical maximum Feminists pushed for. And Conservatives like the centrist Simps they are, still tell you that a proper Trad Lifestyle means you gotta marry the woman. Which means to do it through the state. Despite the state only having that responsibility for a few hundred years at best.
The best thing we can do to help men, their families and kids, is to push the concept that you can pirvately marry a woman without the state. We need to make it socially acceptable. We need people, who say that, who live that.
But sadly we didn't do the homework. We could have website, with replacement contracts, which equalise private marriage with state marriages. Like a letter of authorization so that as a privately married couple you have authority over your partner in medical emergencies (sorry I am German, I dont know the exact translation for it). Stuff like that. We could have had websites, where we explained all of the different contracts as replacement for state marriage, have all of these documents ready to be printed out. It would be important to give this all the appearance of social legitimacy. Because women care about that. Which is why I also say to marry her in church and give her a nice ceremony and also to properly adress her as your wife after that and to shut everyone up, who casts any doubt upon whether that marriage is valid.
I think the reason we don't have that, because many Conservatives are basically Simps, who would even push for state marriage, if it means the woman could castrate you on divorce, because "You just weren't man enough to keep her".
Please let's keep this about the legal aspects. Let's not muddle it by talking about how you should be more masculine towards your woman, keep her pregnant 24/7 or whatever. The legal aspects of marriage are still there, whether your wife is a perfectly happy and satisfied waifu or not.