I am trying to use a transitional phrase to link the following paragraph back to the main idea. I am writing about the 3 kinds of schools, private, public and homeschooling. I just wrote about Public now I am transitioning to talk about Private.

Question

My paragraph begins:
However, Private schools require students to wear uniforms and operate differently than public schools.

My question: is this a good transitional phrase? If not how can I correct it?
Thank you,
Jonathon

Answer 1

[ I am not sure all private schools require uniforms. ]
In contrast to public schools which are free to the families of students private schools require tuition as a rule. Moreover private schools can limit their student body to good students or good football players whereas public schools are open to all.

Answer 2

╱▔▔▔▔╲
 ╱  ╭┈  ╲╮
 ▏       ▔▔╲
╱╳╲   ▍ ▍   ╲
▏╳╳▏     ╭━╮▕
▏╳╳▏ ▏   ╰━╯▕
╲▂╱╲ ╲      ╱
   ▕▃▃▔▔▔▔▔▔
   ╱  ╲
 ╭┓▏▏ ▕
 ┃╰▏▏ ▕
 ╰╭ ▏ Snoopy