In many cases, mobile versions are stripped down version of a regular site, fewer (and smaller) images, larger space between links for use with touch screen, and so forth. A good resource is Developing mobile sites [support.google.com]
As for the detection script to redirect visitors, I personally recommend you do not use one. It is better to give your visitors a choice by having a link at the top of your regular site saying something like "Mobile Friendly Version" and one on your mobile version saying "Full Site" rather than forcing them. Except for "dumb" phones, virtually all new smart phones can view a normal web page. The advantage is offering a mobile version is so they can use less bandwidth.
And if you do a web search, I know there are mobile friendly dynamic menus available that rely solely on CSS and are spaced for use with touch screens. I just put one on one of my sites and it is really nice.