How do you get the blueprint images to fit properly? It seems they have to be a perfect square or something. My images are rectangular and when brought it they are squeezed lengthwise. Any way to avoid or fix this? Should I not be using the blueprint object for this?
Yep, that's one of the main ways I've done it too. Making the images square. You can also figure out the aspect ratio for the images and enter that as the height and width size. One other way I’ve done it is to make as second temporary version of my image and place something I know the size of, typically a square. This is especially useful for sizing an UV texture to an exact size to match a real world measurement (I do this with brick textures all the time). Some people use those color grids you've probably seen before for UV mapping. Those can help to get the aspect ratio correct on a UV map.
One other way to do this is to create polygon planes the size of your image and then apply an image material to each one. A little more fussy, but this gives a little more autonomy for each view to be placed and sized where you want.
Actually one could just type the measurements of the pic into x and y in the properties of the blueprint object, for example x = 1.92 and y = 1.08 if the picture is 1920x1080 pixels ...
When I use background-images for modeling, I don't care about the measurements of an object. The finished model I always scale down to the real measurement, in Cheetah with the help of a proxy object like Swizl mentioned.