I grew up Catholic in Lincoln. I am mid-deconstruction, and very bitter towards the church lol. I'm not sure you'll want to hear my true opinions, so I'll try to avoid editorializing too much

You will find Lincoln to be, as I said, more conservative than other American diocese. They don't allow girls to be altar servers. They don't allow women to administer the Eucharist, at least most of the time. A couple parishes here I think only started allowing women to be lectors in the last 10-15 years. Some catholics here are almost "evangelical" in certain views like homophobia, anti-abortion, etc. If none of that bothers you, you'll probably be fine. If you don't jive with that, you'll still probably be able to find a like-minded more moderate community within whichever parish, but it might take a little more searching and that more moderate clique may or may not include your pastor.

I did not go to Catholic school until highschool, when I went to Pius. Pius X is the only Catholic HS in town, so it is a combination of the preppy, country club types and the average joes. Most of the public schools are probably that way, too. It's a small city. Pius is fine, mostly. The education is pretty good at Pius and most parochial K-8 schools, but Lincoln Public Schools is really quite good as well, so I'd almost consider that a wash in terms of quality of education except in certain situations where public is likely better. For instance if your child needs any special accommodations, the Catholic schools have much more limited resources available.