You need to kill the blackberries 1st for best results. Since you are in Va, you have a latter fall so you still be able to kill or at least get the first spray of Glyphosate on and still seed and get the grass growing before winter. You may/probably need to SPOT treat the blackberries as they try to regrow this fall and next year. If on level ground do not use straw because of all the seeds found in it. If on sloping ground, try and get "Weed Free Straw". or make your own by spreading straw on blacktop or concrete and watering it everyday to stimulate the seeds to germinate. After two weeks, stop watering. Let dry, and then use as mulch.After watering for two weeks there should be few if any seeds left to germinate and become weeds.