IMHO, anything autonomous really. The Pilgrims started The First Congregational Church of ____________(fill in city/town). Last I knew, the one in my home town was still independent. Many went Unitarian in a split. Baptist but not Southern Baptist is similar.
With autonomous/independent, it’s really a matter or the preacher and flock. Same with non-denominational. Could be good or not.
I’ve never seen a Congregationalist outside New England. Seriously. Never heard of them until I moved up there (and I have roots and relations up there). It’s everywhere there but nowhere down south.