First identify which unwanted plants are growing there, because some may need to be dug out and not simply covered up. Vinegar, if the right stuff is used, may kill the top growth of any plant it is sprayed on, but often those plants regrow from the roots which are not harmed. Newspaper or cardboard plunked down and covered with another material to aid in holding it in place and hiding it. Since covering unwanted plant growth is as effective as spraying with vinegar I would not do both.

kimmq is kimmsr

I have done similar jobs, and what I did was figure out which of the weeds must be dug up, as kimmsr says, and get digging. Depending on what's left after that, the vinegar may or may not be effective - if the weeds are perennials, they're coming back. The benefit of the newspaper/mulch combo is that after a year, the soil underneath should be nice and soft, and you'll be able to pull the stragglers out easily. As long as it's not anything with runners, like mugwort or some of the grasses.

If one is going to smother, no kind of chemical/vinegar is needed.

Smothering works, except when it fails for one of several reasons, which you'd want to avoid:
Woody stumps poking holes.
Seams not overlapped enough.
Disturbed too soon.
Not covered with enough mulch/leaves/other organic material to add enough weight & completely block the light.
Thin layers of newspaper used for plants that are strong enough to come through. I always use corrugated cardboard.

Later maintenance fails that can seem like smother fails:
Lack of borders.
Mowing seeds back into beds.
Failing to pull unwanted plants, (usually via bird-dropped seeds,) and letting them drop new seeds.