If you can, and unless you can automate irrigation and put a lot of water on the new lawn? Wait now to plant until fall. You know what could happen to us in the Midwest heat and humidity wise from now through mid-September! Establishing new turf is doable in hot weather but it adds to the challenge.
You could think about applying herbicides that would kill the weeds and weed seeds you have now this summer. I honestly do not know which of the general and non-selective soil preparation chemicals are available here. You can also RoundUp spray the existing weeds but you have a fairly large plot of land.
You should get a soil test so you know what you need to add come fall to balance out your soil.
In late summer or fall you will want to till the existing soil and fold in any amendments indicated by the soil test. You can rent a heavy rototiller for a day or hire someone to come in with one or a small tractor if you have access. You will have to get estimates to see what the going rate is.
Make any grade changes needed to improve drainage. Pull out any rocks, weed clumps, etc and level the seedbed off nicely. Install an irrigation system if you plan to do so but leave the sprinkler heads above grade.
If you plan to seed or sod the new lawn, you should lay down a starter fertilizer according to package directions. If you plan to hydroseed, which I highly recommend, the fertilizer will be in the slurry.
Now if you are going to use seed you will distribute the seed evenly, top dress and roll with a half full landscape roller so seeds make firm contact with the soil. Keep evenly moist until it germinates. Use a good seed mix of perennial (not annual) rye, bluegrass and fescue. Rye will germinate in about 7 days and the bluegrass and fescue may take 14-21 or more depending on moisture and temp.
If you are laying sod. Make sure the sod is fresh harvested and no more than a day old. Get it delivered the same day harvested if you can. Water it as you install it---don't wait until you are finished! When all is installed, roll it with a half full landscape roller to put the roots firmly in contact with the soil. Remember sod is a transplant product and you will start off watering just to keep the cut layer alive. Don't over water or you could drown it. Slack off and shift to watering longer and less frequently as it establishes.
As mentioned, hydroseeding is a great alternative to planting turfgrass. It is a fraction of the cost of sod and will establish faster than either a seeded or sod lawn. It adheres nicely to slopes and grade changes. A slurry of fertilizer, seed and mulch is sprayed on the prepared seed bed to form a crust. All you have to do is keep it moist until the seeds have germinated. Look in the phone book for hydroseeding contractors and you can go ahead and get on a fall schedule. If you want to try to plant a lawn this summer, hydroseeding is definitely the alternative I would try.
When your turf starts to establish mow it at the tallest setting. Among other things, tall thick turf is your best defense against weeds. With young, still shallow rooted grass shoots you want to make sure your mower blade is sharp or you can literally yank the grass blades out of the ground.
Once the turf has started to establish and the ground has settled, lower your sprinkler heads to grade.
As mentioned, gradually increase your watering schedule longer and less frequent to encourage deep root growth. In the industry we sought to provide the equivalent of 1" of rainfall per week. Never water later in the day then grass can dry out. Insects lay eggs and fungus spores take hold in damp, dark turf.
If you plant in the summer or early Fall you will want to start on an annual feeding routine with the late Fall fertilizer application. Then start your feeding and herbicide program again in the Spring. Having been in the turfgrass industry the cost of the Scott's program always causes me a double take but I guess the pretty pictures on the packaging are worth it. It is rather foolproof though and you cannot go wrong following it.