Pull the weeds once, mulch thickly with wood chips ( free from any tree guy) and plant some native flowers like black eyed susan. Turn an eyesore into something nice for your neighbors.
Cherry

Nothing that "sterilizes" the soil for a season is anything you want to be spraying :-) Just as likely to sterilize you (or worse) as well. Use a gas-powered string trimmer (heavy duty model) and cut the brush down. Then spray with RoundUp or other broad-spectrum herbicide of your choice. The herbicide will be much more effective on the cut/exposed plant tissue. Since herbicides like RoundUp are most effective on actively growing plants, your window for doing this with successful results is shrinking.

Unless you do something else, the weeds and brush will return. It's just a fact of nature. Mulching heavily with wood chips will slow the process, but I'd consider planting the area with some sort of low maintenance groundcover for a longer term approach. Bare soil will sprout weeds - it can't be avoided.

I disagree with you Gardengal, an organic choice can be found in high acid vinegars. they kill down nonselectively and change the soil pH beyond adaptabilty of most plants.