To keep things simple at this stage, in order to draft an initial application list, the list @merc81 cited in #27 can be pretty useful. Most of the ~60 schools on it (including Rice) are competitive for quality and net price for a high-stats, middle income student (~$80K family income) after adjusting for need-based aid.
https://www.usnews.com/education/best-colleges/paying-for-college/articles/2016-09-19/colleges-that-claim-to-meet-full-financial-need
A typical net price at those schools, for that income level, assuming financial assets ~equal to annual family income, and 1 child, might be about $15K-$25K/year. Examples:
$13,700 Colorado College (with $40K home equity)
$17,092 UChicago (apparently doesn’t consider home equity)
$24,050 Harvey Mudd (with $40K home equity)
$25,930 Northwestern (with $40K home equity)
YMMV. Net prices can vary by thousand of dollars depending on travel costs as well as home equity and other factors.
Now, for some of the listed schools, high stats are necessary but not sufficient (and “high” means really high).
Many of the somewhat less selective listed schools are small liberal arts colleges, which IMO are great but not for everyone. Also, many of these schools offer little or no merit aid (or, if they do offer it, would require extremely strong qualifications to get it). For your match and safety schools, it may pay to focus more on schools with relatively low sticker prices or that offer big merit scholarships.