I'm using the standard way for the site I'm working on now. The main reason is that desktop and tablets are the majority of visitors. Mobile is up and coming (and catered for, don't worry ;) ), but it made more sense to start from desktop in this particular case.
Other than that I would say that mobile first is better, mainly because it will focus you on what has priority on certain page. And from there it's easy to move into multiple columns when you have the room :)
Design shouldn't be done in Photoshop anymore, at least no full comps, more like styletil.es. Designing with code is much easier to do in my opinion.
So in your case, I'd say go mobile first, design it out there and adapt the site for the various widths with media queries.