As a computer junkie turned Radiology researcher I have to say...
The laptop you choose really doesn't matter that much. I think people put alot of emphasis on the latest and greatest, but in reality there's very little difference in performance between year old technology and brand new technology except for whopping changes in price to get the latest stuff. In any case, my research lab and the others I interact with are split between PC (mostly Dell) and Mac. I've always liked PCs better because they just have more applications developed for them, though Mac has always been strong in the image processing world. All the apps you're likely to use (Photoshop, ImageJ, IDL, diferrent DICOM viewers, etc) will have Mac versions. I would choose based on what most of your lab mates have, and if they're split, go with which you like. Personally I have a fully loaded Inspiron 9300, which at the time (a little over 6 months ago) had just about the same features as the XPS (sans the stylish case) but for about $1000 less.
But, if we're going to get into the nitty gritty, the following disclaimer applies: certain things are going to depend on exactly what kind of processing you're doing, so it's hard to generalize. On the processor side, I run alot of custom jobs in IDL and ImageJ, and I think any modern processor is going to handle that just fine. You're not going to see much difference among them. You probably won't see much difference when it comes to 3D rendering either. For those reasons I would say to save your money on the processor (buy the lowest for whatever model of laptop you decide on) and put that money into other things.
Make sure you have at least a gigabyte of RAM. It really helps if you have alot of operations going on. I'm yet to see a Radiology imaging application that really stresses a video card. As far as I can tell, the only thing that really stresses the modern video card is a video game (i.e. my World of Warcraft addiction). In any case, avoid video cards that don't have their own memory and from there decide if you're ever going to want to play games on it (if you do, go for the best video card, if not... middle of the road is fine).
I have a 17" screen on my laptop, but I know others who don't wanna lug such a monstrosity around. So the other option is to buy a smaller laptop and then buy a LCD for your desk to plug it into. That's something you have to think about. Personally, I would never want to have a 14.1" or 15" and have to stare at it for hours on end with all the windows I usually have up at once. The image resolution really isn't going to matter, as all modern laptops are high enough for this application.
I think a DVD-burner is becoming increasingly useful, especially since images tend to take up alot of hard drive space. Hard drive storage itself is also important for all that data, though your lab should hopefully have some sort of network storage.