Need one to run Lightroom/photoshop.  Should I be looking for PC or Mac?  Any recommendations that can effectively run this software?  Budget is around $1200.

I finally switched over to a Mac about 18 months ago. I will never go back to Windows.

http://store.apple.com/us/browse/home/specialdeals/mac/macbook_pro/13

Photoshop/Lightroom? Either Mac or Windows will be fine. Depends on what else you want to do. Surf the web at home/work and already have an iPhone/iTunes/iCloud/iWhatever? Get a Macbook Air. Interested in something a little more versatile? Check out a Microsoft Surface 3. Personally, I would go Surface for the versatility but I also love tablets/hybrids... Fantastic when shooting/composing tethered to a DSLR or airbrushing a photo in post. Id take MacOS over Windows 8.1 though Windows 10 will be a free upgrade this summer and seems pretty existing as far as operating systems go.

Regardless, you cant go wrong with either.

Do you want a lighter/smaller more portable laptop with a longer battery life or a less portable laptop with shorter batterylife but much more powerful?

Agreed...once you go mac you never go back...

I did...went for a Pro Retina.  Love this thing.

 

I cannot speak to the macs, but on the PC side you basically would be looking for a gaming rig with lots of hard drive space. Gaming and media processing need the same video card and screen abilities.

I personally would look for a desktop for photo editing.  Or else get a big LCD screen that you can hook up to the laptop.

Regardless of OS, OP definitely doesnt need a gaming/workstation rig. Adobe software (since CS5) fully supports Intel's HD4000 and newer integrated graphics for GPU acceleration. That said, an i5 (photoshop benchmarks) with 8GB of memory would be very comfortable for photo editing. Thats not to say theres no benefit to going bigger and faster, but thats where you run into diminishing returns/value.

An external monitor isnt a bad idea, though, and would let OP get a portable 11" computer (Macbook Air or Surface) and still have large screen to work on in a more permanent space.