If you are trying to save money, I would nurse this weed patch through the summer and spend your money and time on it in the fall - late August. Now is a poor time to seed new grass because it does not have time to develop sturdy roots before the summer heat hits. Secondarily, if you seed and do the proper watering now, all the crabgrass seed will germinate and take over the lawn by July. If you just start watering proper for a mature lawn now, you'll be surprised how much better it looks.

Having said that, if you want a bermuda lawn, then you should start in June or July, so I wasn't thinking of that in the previous paragraph.

Set your mower up high. Tall grass and weeds will shade out the lower growing grass and weeds. It also looks more lush when tall. And again, this does not apply if you want bermuda.

Proper watering for mature grass is deep and infrequent. Deep means a full inch as measured by empty cat food or tuna cans placed around the yard. Infrequent means once every 2 weeks this time of year and once a week when the temps get into the 90s every day.

Mulch mow when you mow. See if you can identify the weeds and plants growing in the lawn so you will know which herbicides will work best when the time comes to renovate.

Fertilize with anything, but if you want to improve the health of your soil, use organic fertilizer at least once a year. I use it all the time and life has gotten much better, lawnwise. If I have any lawn issues, I'm confident that poor soil is not the reason.

What are the big round green things in the yard?

Green round things are probably septic covers. We just had ours put in so got the same LOL