Automated tests for 3 x frontend systems

We have 3 frontend systems based on backbone.js and nunjucks templates, talking to one central REST API. The frontends range in complexity from ~6 screens, to 20+, some with modals, inline alerts etc. The job is to set up automated tests for them, which the team could then take on and extend in future development. We're currently running an in-house install of Jenkins on an Ubuntu box to run tests using [login to view URL] against the REST API, and the frontend tests would also run as Jenkins projects, if done in selenium then with headless browser. We have in-house skills to help with setting that up. Some other frameworks we've looked at were casper and zombie, but couldn't get them to work, I think largely due to the architecture of backbone and client-side templates being nontrivial for them to parse/render. Further work we'll be looking at is automated testing of iOS and Android apps too, quite likely using monkeytalk. I think a good approach would be first get you logins to our staging environments, so that you could get an idea of what's involved, ballpark quote, then try out getting tests in place for the simplest frontend first, and take it from there.