It actually really depends on the software. It is especially important to do some research here because some graphics card have really big power requirements, and your computer might not be able to accommodate any of them. Make sure to compare the specs of your power supply to those of the graphics card.

To my knowledge Lightroom is not GPU accelerated (see requirements), but it is heavily multi-threaded (the more cores, the better). Apple Aperture is accelerated in that it uses "Core Image" on Apple hardware (see requirements). As Matt pointed out, some parts of CS4 are GPU accelerated, and this is even more true for the whole CS5 suite. If you have a Video DSLR like the Canon 5D MII, processing large photos and huge videos can be very tricky without the proper hardware. With the introduction of the Mercury Playback Engine in CS5 Adobe delivered some serious hardware acceleration; if this is something you see in your future, you might want to check the list of supported cards for CS5 early on (and how to enable more).

As a rule of thumb in Photoshop, the more memory on the graphics card, the more "accelerated" documents you can open at the same time. Opening one large photo (say > 20MP) shouldn't be any problem with any modern graphics cards.

I haven't heard of any differences between LUT performance between graphics cards either; as long as your monitor is properly calibrated, you should be fine.