Good suggestions in this thread. My $0.02 of input is that you shouldn't feel embarrassed about your yard. We all start somewhere, and with the information and help that I got from this forum, I'm getting closer to the yard that I want.
What's going to be easiest for the lawn to thrive is to reduce the weed pressure off of the grass as much as you can. Get your pre-emergent(PreM) down ASAP, this will help you combat the summer weeds that are going to hinder any progress that you make the rest of the year. Once you get the weeds dealt with, then focus on getting your soil in optimal condition where you can have good success with next year's work.
What's going to be most helpful
is getting your soil test, and that will dictate on what you need to fertilize with. St. Aug likes a different pH over Bermuda. The test will help you determine what amendments to make.
Take the time to read up on the cultural practices for Bermuda, if that's the grass type that you want to encourage. Mowing is going to be the best cultural practice that you can practice, and Bermuda likes to be mowed low and often
. You don't have to spring for a greens mower, just get a push Scott's reel mower off of Craigslist, or a new one from Home Depot. It's $99. That's what I started with.
I'm giving you these points of advice, because that's exactly what I did for the back yard of my house. And when I say that you don't have to feel embarrassed, you don't. The pictures below are what I was able to get with 3 months of work, and letting the bermuda that was there do it's thing. It's even further out right now.
Feb 28th of this year