Your plan is not the best way to go but you’re in NY and irrigation needs are far less than in the sun belt. With your size yard I would go with a conventional system with PVC pipe, back flow preventer, controller and irrigation valves. It will cost more and longer time to install.
You didn’t mention the width of the yard. The 32ETI is a nice little kit for a small yard. For your length do go with 3/4 inch and for each sprinkler tee off with a 3/4 x 1/2 x 3/4 fitting. The issue is the size of the timer. It is designed for 1/2”. Using 3/4” pipe will lower the flow resistant but then you’ll need different barb fittings and then the cost and having the right type of fittings becomes a hassle.
If you really want to use this kit install the kit as it comes to the section closest to the bib and give it a try to see if it meets your needs. As you go up the in elevation the spray distance will decrease. Running six heads in a row with 1/2” the last two may not have enough pressure to work as the expected.
Rainbird.com does have a design aid program. Plug in the numbers and see what they come up with. I’m doing this from an iPhone otherwise I would draw out another recommendation.