Outputting front page to a different url
I would personally suggest putting breakpoints into the CSS and making the site adaptive. You would save yourself a lot of time building a separate mobile site.

Plus, especially with adaptive widths, and not fixed widths, you allow your site to display nicely on all sizes of device screen, and when a user reduces the size of their browser window on a desktop.

Alternatively, To detect a device and show a different site e.g. m.yoursite.com have a look at this answer.