This project actually didn't have much stone or gravel, but it did have large expanses of mulch the first year (as seen in this photo). Ultimately this project was planted densely so as the plants mature, there won't be opportunity for weeds, but the first year did require significant maintenance from the homeowner.

Gravel paths can require a lot of maintenance too if they aren't frequently traveled because it's prime opportunity for many weeds (low competition). Pre-emergent herbicide can help prevent annual weeds seeds from germinating, but if you prefer to avoid chemicals, regular maintenance (pulling, clipping, horticultural vinegar, or fire) is still necessary.

Where do you find horticultural vinegar?

Most independent garden centers or garden supply stores carry it. I think it's appropriate for use on a path but I personally don't like it in the garden. Even though it's "organic", it's still a strong acid and I am afraid it would mess with the soil biology too much.