I would go to the local home depot or someplace that rents an aerator.
Be mindful, it's a lot of work using an aerator. Then seed over top
using a broadcast spreader. Also apply starter fertilizer.
Make sure you keep the seed wet, watering just about everyday. You
should see some excellent results in the spring.
Personally, I use nothing but Lesco Products, to include their seed
(Team Mates) It works well for me. I heard of their products from a
buddy of mine who is a landscaper. (www.lesco.com for a dealer near you)

I had problems with broad leaf until I went to Lesco same with their
Dimension Crabgrass Herbicide. They actually have a pre-emergent and a
post-emergent in their product so even if you miss the window for
applying it, it should still work.
Good luck