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Potato sizes: Based on what I've been buying here (in Europe) for the past 10 years I define potato size as follows:

New or very small: 1" round (2.5cm) 1 - 2 oz (45gr)
Small: about the size of a golf ball or 1.5" x 2" (3 x 5cm)  3 - 4oz (150gr)
Medium: about the size of a woman's fist - 2" x 3" (5 x 7.5cm) 5 - 6oz (175gr)
Large: bigger than medium -  2.5"x 4.5" (8 x 11cm)  7 - 8oz (225gr)

We don't have anything the size of the monster 16oz (500gr) 'baking potatoes' one can get in the U.S.

Cutting techniques referred to:

Salad:  Slice potatoes - the long way, first in half, then in half again.  Now slice (the short way) about 1/4 inch thick.  We are aiming for bite size so if you have a huge potato, adjust accordingly.

Roasted:  Slice potatoes - the long way, first in half, then in half again, then in thirds or fourths the short way.  If small potatoes cut in half the long way then in half or thirds the short way.  Very small potatoes leave whole or cut in half.

I don't peel potatoes.  I think it's a waste of time and nutrition (exception for garlic-mashed).  Peel if you want to.

To store: 

Keep potatoes in an open container in a cool, dry place away from onions and garlic.  Do not refrigerate. 

Cooking Potatoes:
     For recipes see Vegetables