Your ideal size is really a range. I don't know what that is, but I can comfortably ride a bike that is 54 to 58 cm, maybe smaller and bigger. I've discovered I like short bikes, which is nice for me because they're lighter and stiffer, and they fit into cars better. I'm 5'9.5" tall with very short legs. Your ideal size may between 50 and 54 cm. Measure your pubic bone height, aka PBH. One rule of thumb is to multiply that by 2/3 and you'll get your ideal road bike size. Then add or subtract 2 cm.

That bike on amazon looks ok but I don't like mail order bikes, especially for newbies. Get a used bike on Craigslist and fix it up or have a local mechanic fix it up.