What to use to kill brush but not weeds?

Trying to tame some raw land I purchased. Plan is to eventually make this land into yard but not right now. I'm trying to find a way to keep the brush (blackberry briars, woody bush) from growing but not kill the grass/weeds in the process. Hoping that the weeds will choke out the brush if I allow it to grow. Any ideas?

I bushed hogged and sprayed it with Grazon Next last year but it killed everything. This year there's not as much brush but it's still there.