Could you be a little more specific of "don't think marriage should be a government function at all" means in the real world?
1) As you said, I would eliminate all current laws.
2) I would make a bunch of fixes that should already be done. The death tax is evil, no one should have to pay it. People are already having massive births out of marriage, parental legal rights/responsibilities should be clarified anyway. And that would assist eliminating "marriage" as a government function as well.
3) As for things like if a woman is quitting her job, the couple could have a contract. I love you honey, I'll raise our wonderful kids. On the other hand, if you leave me for your secretary you rat bastard, than I want half our pile and income for 10 years, or a third, or it all, or whatever they agree to. Of course they could amend it over time by agreement. That contract is what courts would enforce.
3) Marriages would be performed and recognized by whatever religion/association you like or just between you. So let's say you are Catholic. The Catholic church can say if you want a Catholic wedding, then you go to pre-marriage counseling, get the blessing of the church, etc as they do now. They could also have a Catholic wedding contract if they want one. It could be rigid or just require certain terms be included. If you want the Catholic wedding you agree, if you don't you pass and do your own, which they may chose not to recognize.
4) Contracts can be between any consenting adult who wants them. Man/woman, Man/man, whatever.
5) I am a strong believer in our having a "Federal" government, not what we have. I'm referring to the actual definition of the word, not how it's used today. Power divided is power checked. So I would not force but would favor States to following it. As for the Federal Government, all citizens should be treated the same, meaning there is no difference between any citizen regardless of marriage or other factors. We are individuals.
However, regarding the full faith and credit clause, I would require each State that does have "marriage" to be able to state their definition in a "contract" covering what their marriage entailed when the contract was signed. I phrase it that way because if the State changes their definition, the Federal government would not recognize the retroactive changes or require States to enforce those changes. When you marry, you should only change the agreement by choice of the parties involved. I would also require the States to honor each other's contracts so someone can't move out of State to get out of their agreement.