When my ex and I split up we tried the week on week off thing, didn't work for our children as they felt it was to long to be away from either parent, as well as their pets at each house. We went to a two nights a week and every other weekend schedule. It worked great for all of us. The kids thrived knowing that both of us were involved and that they were loved by us both.
We also each stayed in the same school district, living less than 3 miles aaprt, becasue I lived across the street from the middle school and 1/2 a block from the elementary and high school, the kids often came to my house everyday when they got older, to be close to sport practices, band and other functions, drop off their stuff, get a snack and head to practice.
We did get prescriptions split when they were written, and double retainers, and split things like contacts so the kids did not have to remember them daily. Likewise they had music stands and sporting equipment at both houses, and even had two sets of ROCT uniforms to ease the stress of transitioning.
Regardless of the schedule you pick, your child is going to be happier if you both are able to get along and co-parent. With this schedule we were able to touch base frequently and the kids saw us working together for their benefit.
Good Luck, I am certain there are lots of ways to do it, that can work if you all want it to.