Mobile Site (e.g. mobile.mywebsite.com)
Given that the primary target audience here is mobile users, what is recommended is a website that is not just responsive – but also mobile designed to start with. This would entail a subdomain (something like mobile.mywebsite.com) – mobile users automagically get redirected to the mobile site.
This solution customizes the user experience for mobile users much more than a purely responsive website.
For a responsive website design, the device does the work by automatically adjusting the display to match the device’s screen size (large or small) and orientation (landscape or portrait). While this is flexible, it is also not as customized as the Mobile Site user experience.
Responsive doesn’t mean that the text and images will be readable etc. The main advantage of Responsive is that it is future-proof – if devices change their resolutions in future releases, the site will still be able to adjust/scale accordingly. For a mobile site, there might be some rework entailed.