I've managed to develop some code in php which would use a mobile template instead of the default one, however I'm not sure if I should redirect to a mobile URL (such as /mobile/) or if it's ok to just have the mobile template showing up instead of the default.
Any thoughts on this?
This is up to you.
Some sites put there mobile view on its own domain, e.g., m.yourdomain.com or yourdomain.mobi, and if a mobile user arrives at your non-mobile site (and are detected via agent-string) they'll be redirected to the mobile domain.
However, Tim Berner-Lee states:
It is fundamentally useful to be able to quote the URI for some information and then look up that URI in an entirely different context. For example, I may want to look up a restaurant on my laptop, bookmark it, and then, when I only have my phone, check the bookmark to have a look at the evening menu. Or, my travel agent may send me a pointer to my itinerary for a business trip. I may view the itinerary from my office on a large screen and want to see the map, or I may view it at the airport from my phone when all I want is the gate number.
There's something to that. This seems to prefer a non-redirection approach but, instead, detecting the agent type and displaying the appropriate view.
Which approach is better is up for debate.
You could combine the approaches by having your main site respond with views based on agent type while also placing content in a mobile-specific domain (not duplicating it, just mapping the additional domain to it), which will allow phones that don't send a mobile user agent string to view the lighter mobile site.
Both approaches are equally valid. Just make sure, for usability sake, that you give the user that ability to switch between the two views and make it sticky. That way, someone on their iPad doesn't always get the mobile template and someone who gets a url to the mobile site can switch back on their desktop.