My understanding of vinegar as a weed killer is that it only kills the leaves that it is applied to. Vinegar will kill the stuff above ground but won't necessarily kill the roots of the weed. It also won't stop weed seeds from sprouting. I get the whole Monsanto hate thing, but I quite like my roundup. Roundup is so effective because it is drawn into the whole plant killing it all and any other shoots that are connected to the same root system. The patent for roundup has also expired so other companies are offering basically the same product but without the Roundup name. Lately I have been using a product from
Hi-Yield that is an "everything" killer. After about 7 days you can replant in the area that was previously sprayed. I also found some stuff at a seed supply place (Steve Regan in Murray) that would do the trick for a year. Both are concentrated and need to be cut down. I use a 2.5 gallon sprayer to apply them.
When I moved into my house the back yard (8800 sqft) had weeds as tall as the vinyl fence. I chopped them down and applied the killz all stuff a few times and was good to go. The front grass was mainly weeds too. I applied the killz all to it twice then re-seeded and it looks fantastic.
If I was putting down gravel and had something on hand I'd spray it before I put down anything but in reality you just dug out the area so there probably aren't weeds are seeds there anyway. The biggest benefit you will do to keep the area weed free is to use a high quality weed barrier, something contractor grade preferably.
This is what I used when I put pea gravel down 18 months ago for my dogs business area. You can get it at some of the local nurserys, I have seen it at Millcreek Gardens and I think I bought mine at Steve Regan.