Replace front yard?

[Doug McLeod]

One of the properties I bought this year has a front yard eaten up with (or made up of) a grassy weed similar to crabgrass. The HOA is all over me and the renter about knee-high weeds, but they get that way in 3-4 days with their seed pods. St. Augustine grass is the standard around Houston. What is the most economical way to get rid of these hearty weeds and re-establish the St Augustine? Almost seems like the weeds need to be plowed up first.