Pros: you will be able to get a proof of concept and a final version of the site quickly, compared to other frameworks. It will be possible to get it developed by a good freelance developer instead of a whole development team. Also a site to rate local schools has fairly standard components, so it would be easy to take existing code from other projects and get it started quickly.
I estimate for example that a proof of concept can be developed in about 3 weeks and a final site launched in 2 months
Cons: Rails developers are more rare than php programmers. Also a Rails application is an elaborate system. It's not as easy as a Wordpress site where you just grab and drop files. You will definitively need someone who has experience delivering elaborate sites like the one mentioned.
If you want more advice, we can discuss.
Obviously a technology fit is on a per-case basis, so it's good that you're asking questions first before just shoving a technology solution at a problem.
Couple things you want to consider when making a technology fit:
1) How difficult is it to find developers who are knowledgeable with the tech?
2) How expensive are these developers?
3) Are the features of the technology in line with the solution you're trying to build?
4) Are the caveats of the technology preventative of you completing the project?
5) How easy is it to leverage community solutions and not reinvent the wheel on common tasks?
6) How difficult is it to support and maintain the finished product?
7) How well maintained is the technology by the community?
Contrary to what you might think, Ruby actually started its life as a bash/console scripting language but was popularized by Rails. The idea of Rails from the beginning was to expedite all the little things that were consistently repetitive in project development.
The Rails community has done a great job of building out a community solution for almost every single problem I can think of. Most API integrations always include a Ruby/Rails integration right out of the gate.
Rails has gained enough momentum over the years that there's quite a large group of international developers as well as domestic, so finding someone to work on the project is pretty easy.
Hosting a Rails app is almost as painless as it can be, provided you keep the implementation pretty vanilla. Heroku offers free development tier project hosting, which includes Postgres DB support, so you can get started for almost no cost.
The common saying a few years ago was "Rails doesn't scale". This is true to some extent, and I really would consider a number of other platforms first before choosing Rails for things like chat messaging systems or highly-concurrent applications.
This doesn't seem to be your case, and your project looks pretty basic from a schema / interaction standpoint. I'd say Rails is probably a really good technology choice for the job, and it should help speed up development quite a bit.