@DashtiBarchi i - You sound like a very thoughtful student. Good luck to you. Since you want to limit how many applications you submit to 10, I would recommend that you focus on matches, and only choose your top 2 reaches. And I would put Williams and Amherst as “reaches” for just about anyone, since their admission rates are 14% and 17%. You are smart to focus on schools with strong academics but admission rates closer to the 30% range.
Here is a brief comparison of Williams and Amherst:
http://colleges.startclass.com/compare/1874-2014/Amherst-College-vs-Williams-College
(You can compare the stats on any colleges you want from the StartClass website.
Here is a list of schools that do not charge application fees:
https://www.niche.com/colleges/rankings/colleges-with-no-application-fee/
This is a great website for college search and financial need information. The woman who created the website offers tons of information, for free, and I found her to be a great resource as I helped my S16 and S17 with their college search. Both of them attend, or will attend schools that meet need: St Olaf (obviously) and Grinnell.
http://www.thecollegesolution.com/list-of-colleges-that-meet-100-of-financial-need/
One thing to consider since you are on a budget and seem to prefer a more rural type setting - It is very easy to NOT spend money, unnecessarily, when you go to school in the countryside. There are way more temptations and ways to spend $$, off campus, when you attend school in a city or large suburb. My S at Grinnell has had a year full of fun weekends, and they are all included in his student activities fee. His only temptation is an occasional Jimmy Johns sandwich, from the location the street from campus. He is very happy to just eat the wide variety of food provided in the dining hall. So maybe consider cross checking your list with the Princeton Review’s list of great campus food!
https://www.princetonreview.com/college-rankings?rankings=best-campus-food
Last bit of advice. For any school that seems to fit a lot of your criteria, complete the Net Price Calculator, with your parents’ help, and see what they come up with. Through both my sons, we found that they were pretty accurate, as long as the calculator asked a lot of questions, making it as specific to my son and our situations, as possible. Many will ask for your GPA and test scores, and will let you know what amount of Merit (versus Need based Financial Aid) you might qualify. It is guaranteed for 4 years, assuming grades are decent, and that is a nice addition to Financial aid.
Since you seem to prefer smaller schools, I would only apply to one (or no) larger state type schools. With your stats and income level you should qualify for a good amount of aid at “meets need” type schools. BUT be aware any school will expect you, as the student, to contribute to the cost of your education, in the form of Federal loans ($3,500 to $5,500 per year), Federal Work Study (about $2,500 per year) and some summer job income (usually for books and personal expenses during the school year, which is on top of the COA Cost of Attendance, at most schools.