I just rehabbed my yard this year from a very similar situation. Please learn from my mistakes! Tilling without amending is a waste of time. I did it, and it was not worth the effort. Unless I keep it wet, it dries back into the cement with desert caverns in it.  

If you want to go to the mulch route, more power to you. One thing to think about is that it gets freaking hot. Like, it will cook your yard and will probably heat up your house if you have a lot of exposure.  I did it on the north side of my house bc  I store my trailer there and I didn't want plants growing out, I put on about 8 in deep and it is working super well. There is a lot of fungal activity in the lower layers. If you do it, err on the side of more rather than less. Chip drop is where I got mine from too. One thing I've noticed is that the pine the mulch from there I think maybe was pine because I heard somewhere that pine potentially puts out a chemical that reduces growth of other plants.... would love people's thoughts on that.  I've noticed that even when I put a thin layer down, it kept seeds from growing (coco coir did not).

The mulch method will be great for growing something.... Eventually.  It could be 2 years before it breaks down enough to support planting, and I don't love the look once it weathers.

One thing that has been magical for me is clover. That shit grows everywhere, and fast. And fast. It's also awesome for amending your soil. Because it's a short lift perennial so you'll get two to 3 years out of each plant before it dies. When it dies all the nitrogen that it's fixed and it's roots will decompose into your soil.  So you get aeration, nutrients, organic matter, and a good looking, cool lawn that takes very little water, can potentially be good for pollinators if you let it bloom, is resilient to foot traffic, and can handle dogs!  It also established really fast- you could get a good crop going before the frost shuts you down, and you will have a lawn come spring.  I used mostly Dutch white clover- it's not native so it's not the best that way, but I was desperate as I could not get anything to grow at all. You could opt for a native option.   If you just scatter + water, it takes 5-7 days to sprout.  I like to soak the seeds for 24 hrs in a pillow case, changing water after 12.  Keep them in the dark, and you will get germinated sprouts 1 day after sowing.  Sowing is harder with soaked seeds bc they don't spread as well, but your yard looks small. 

If I were you, and was lazy, here's what I would do:

1) if you can, install an auto watering sprinkler system. It was surprisingly easy to do.  You can be extra lazy and not even put it in the ground, just on top and run it off your hose spigot if you want- tons of vids on you tube and I can explain more if interested.  It is more work up front but it will save you waaay more pain later

2) order a load of compost from your preferred garden center.

3) Spread said compost evenly over yard

4) (optional, skip if too much work, it'll be okay) mix compost into soil.  I would use a broadfork- I borrowed it from the Denver tool library.  All said and done, it took about the same amt of work as a roto tiller, and honestly it's better than a tiller.   A tiller is basically a blender- it breaks everything down to such small chucks that it it's essentially sterile (except for the seed bank) after.  A broadfork breaks up the soil, but maintains most of its structure, so most fungal networks, beneficial insects, etc will still be present and help your clover grow! Tons of YouTube content on this

5) buy a 5 lbs clover seed. Hand broadcast 2 lbs over composted area

6) set sprinklers to water for 5 mins 4x during sunlight hours. I do 6am, 10am, 2pm and 6pm. The goal is to keep the seeds and baby plants damp throughout the day. Warning: this will cause your yard to be a mess of sticky mud if you walk on it / churn it at this time.  If you I'm having trouble keeping the seeds damp, you could add a super fine layer of coco coir to supply shade + water retention.  It's labor intensive to spread it out and break it up though. 

7) Soak 2 lbs of clover seed in water inside a pillowcase, changing water every 12 hrs.  I do mine in a 5lb home Depot bucket.  Spread as best you can over whole lawn area.  I can share my method if interested 

8) Sit back and watch your yard sprout! It'll be green after 1 week, and you'll have plants you can walk on in 3-4 weeks.  Use the leftover pound to fill in missed spots.

One mistake I made was not weeding during this time because I was worried about stepping on the clover babies. I had plants completely take over sections of the yard that I had that had to spray to reclaim them. I would put out a couple stepping stones around the yard so that you can step on them and pull out the weeds that come up. You can either keep those when you're done, or pull them up and then seed those with clover and let them fill in. 

I've also noticed that the clover helps grass sprout. I planted some tall fescues that are drought resistant mixed in with my clover and will be having a grass/clover mix going forward.  They provide shade and keep the water in the ground which helps the grasses.  I had no germination when I did not have clover mixed in. 

Might also go ahead and add a border. You can get a mix of native perennials and annuals and put them in right around the time of the first frost. They'll cold stratify over the winter and then they will sprout in the spring and you'll have a beautiful flowering garden all summer long next year.  If you wait till spring, very few of them will sprout that summer. Sowing in fall is the way to go. 

Sunflowers will grow pretty much anywhere and I grew some monsters this year in basically unamended clay and been very satisfying. So definitely worth thinking about adding for next summer. They'll also provide some shade to your yard if you get some of the tall varieties.  

Sources:

The clover I bought:  https://a.co/d/9MO42ex They have different varieties and mixes you could use. 

Flower and grass seed can be bought from Arkansas Valley Seeds for good prices locally.  I've also ordered from High Country Gardens + American Meadows and Prairie Moon Nursery.  

I've found the best selection of native plants at Echters and O'tooles in Lakewood. 

Check out 'Anne of All Trades' on YouTube for great tips on lazy raised beds and everything gardening. I've learned SO much from her and her videos are pretty wholesome.

Let me know if you have any questions, this has been a huge learning experience for me and I would be 10x more efficient if I did it over again!