Wildflower meadow

I am looking to convert about 3000 sq ft of my yard into a wildflower meadow. Soil is alkaline, caliche rich but has good organic matter content. I have a ton of weeds growing - silver leaf nightshade, prairie tee are the major ones. The area also has winter grass which is currently brown and dead. I have mowed everything down as low as possible. How do I increase my chances of success? I have a tiller. I am planning to use a wildflower seed mix from Native American Seed (please suggest specific mixes you’ve had success with). Will shallow tilling help reduce weeds? How often and how many passes should I make?