SE Nebraska location for me, same drought conditions
I'd follow Snowhunter's advice but wait til the fall. Weed pressure should be less, temps should be cooler for less watering, and you don't have to deal with it over summer trying to keep it alive. Get a seed that had one grass that grows up quick and another that spreads from a local supplier. I use Miller Seed in Lincoln, NE. Early May is a NE/IA brand, so I'd check there too. You should get some good growth right away that will cover some of the other seed to help it along. Prep the bed, seed, rake lightly to get some soil over it, then roll it with a lawn roller if you have one (I use my ATV), then put out the straw blankets.
The erosion control blankets (net type with straw somehow attached under) are great. Though, I'd caution against assuming they covering the full 8' by 112'. We added a lean to on our barn last year with a lot of new dirt and grading all around the building, and used them to help the grass get established. I'd bet I got 70% coverage versus the measurements, even if I stretched them tight, but I'm definitely not a pro. You can install it by yourself, but having help is a plus. I bought the 16' wide ones and definitely needed help. One can stake while the other unrolls and keeps it tight. Buy way more stakes than you think you need.
For water, I bought some cheap sprinklers at Walmart that I could daisy chain three or four together on the same hose and put them out for best coverage. I used every hose I had around the place, and bought a few shorter ones, but it was better than moving sprinklers around every time. I watered 3X every day, because it was August and hot. Just enough to keep it wet with no runoff.