You need to know the precise standover measurement of the bike, and your precise leg length, crotch to the ground. I'm a bit shorter than you, with a 34 inch inch leg length. With a bike with traditional geometry, my preferred size bike has a standover measurement of about 33 inches (just behind the stem), which yields a size of 57 to 61, depending on which method of sizing is used.

One of the advantages of buying from a good bike shop is a careful fitting before you buy. Buying mail order is advertised as a means to save money. Yet, it often results in a very unhappy customer, who has wasted a bunch of money. A bike that fits you perfectly, from a shop that provides service before and after the sale is the "best buy" in the long run.