You have a described a situation where there is a lot of technical debt from having no tests.
My approach would be:
Change things for all code (new or updated) going forward to have tests.
This doesn't just mean 'require tests', it will mean investing in lots of education, training and introduction of a changed development philosophy and supporting processes.
Currently folks are writing functionality without tests and that is a huge thing to change that will require a lot of effort from all involved.
You may need a coach or contractor who can help you.
It is hard to fully describe the feelings I've had going from before with no tests (terrified of breaking stuff, clueless if I'm breaking stuff) to after with good tests (safe, secure, protected, covered, calm).
Use a code coverage tool to list what needs testing in the codebase
codecov and code climate are 2 examples here
Enter tickets for the technical debt tests
You will need to balance them against new feature/bug development
Use local linting tools
For ruby, rubocop
Use a CI environment to run the test suites
consider having some technical debt weeks to address the untested code
Figure out which Unit, Integrated and User Acceptance tests should be written
One route might be to start with User Acceptance tests using RSpec and capybara against a real browser. This gives you immediate end-to-end testing of all the components. Then I would probably focus on model tests which is where your business logic should be grouped, finally doing controller tests as integration testing.
More on the Testing Pyramid and the Quandrants of Agile testing at https://sqa.stackexchange.com/a/23396/8992