I usually make my borders 1/6th. of the long edge of the print and round to the whole inch. So 8x10 & 11x14 = 2" border, 13x19 = 3" border, etc. I like the look of a 4" border on a 16x20, but otherwise the math holds (for me) up to 30x40.
There are no hard and fast rules, but in general how you position the image in the mat depends on how high you're going to hang it in relation to the viewer position. I think an image viewed at or above eye level looks fine if it's centered in the mat. But if the image is going to be viewed below eye level then I like to give a little more weight to the bottom of the mat by placing the image slightly higher in the mat. I use a simple geometric solution that gives me nice results.
Place the image in the top left corner of the mat. Lightly draw two lines to bisect the remaining white space for both hight and width. This gives you the border width needed to center any image in any size mat. To give more weight to the bottom of the mat, draw a diagonal line from the lower left corner of your image to the far right edge of the mat where the the horizontal bisecting line meets it. Place the lower right corner of your image at the intersection of this diagonal line and the vertical bisecting line (indicated by the red circle above).