Seems a simple thing really, but is it unusual that I just can't seem to crop well in Lightroom? I love it for organising and editing my photos, but I find that if I want to get fine grain cropping for screen or printing then I'm exporting the photo from Lightroom and then opening that up in Photoshop Elements and using the crop tool there as it's easy to set the size and aspect ratio you desire and then drag onto the image. I'm I just not finding this functionality inside of Lightroom, or does it really not exist and you have to use another application for that?
Lightroom gives some good cropping tools, IMO. Press "R" or go to the Develop module and click the crop tool below the histogram (though it sounds like you know that part).
To set the aspect ratio, in the Crop & Straighten tool area is an "Aspect" row, and from a drop-down you can select predefined aspect ratios, create a custom aspect ratio, or just freely crop it without restriction.
You can't crop to a size in Lightroom. When exporting you can specify the size of the image. So: crop to the aspect ratio you want (or to the width/height you want), then when exporting just be sure to enter the size you want to export the image at.