My daughter cast the merit net wide - 7 schools with one being her NMF school. Of the 7 she applied to - 5 were out of state public universities, one her home state flagship, and one mid sized private that impressed her.
She ended up with at least a full-tuition scholarship at all but 2 schools (which offered her scholarships to bring it below their OOS costs but not quite full tuition) based on GPA 4.0UW and 35 ACT score. She is also a NMF. She was invited to three of the schools’ most competitive full ride or full ride plus scholarship interviews. In the end she turned down all the scholarship interviews and pulled out of the process to go to her first choice which was her NMF school.
When deciding what schools to apply to we started with a list of about 40 schools that were strong in her major and offered at least a full tuition merit only scholarship. She then emailed the department she was interested in a list of 10 targeted questions and eliminated some schools based on that. She also researched (and I helped with this) how many spots there were and how competitive she would likely be for the top level scholarship and eliminated a few based on the odds. We started visiting schools and getting feel for them and the “type” of school they were. If NMF is even a possibility I would ALWAYS organize tours through their NMF office as the visits were so much nicer. For her the department visit almost always made or broke a school. It was the most important factor in a visit, second was spending a few hours in the student union and simply walking around campus talking to students.
We decided she could apply to 10 schools, in the end she only chose 7 because the applications and essay writing for each competitive scholarship is VERY time consuming and you want to make sure you did a good job on it. In the end I think she probably could have applied to just 4. Her top three and the state flagship as her safety. Especially since the 4 would have included an in-state safety and a NMF safety. The other two schools that offered her their full-ride scholarship interview and ended up her 2nd and 3rd choice (were in her top 3 from the first list). I strongly encouraged her to apply to one (the other full-ride offer) so she had a smaller school since all the rest were very large and the application process was free and it required no essay - so very little work on her part.
I would really recommend researching your odds for the scholarships and how many are given BEFORE deciding to apply. Then throw your hat in the ring but realize there are often a lot of extra essay and application and interview requirements and many involved unpaid travel.
Start EARLY this summer as many of the application deadlines were the same time and early October - and some are rolling admission starting in the summer and they definitely advantage the early applications. My dd had scholarship offers as early as the second week of September. But then realize a second wave of applications is coming for the scholarships which will also have similar deadlines in November or December.
Good luck and feel free to ask questions!