The *A website
www.staralliance.com has an online mileage calculator that allows you to plan a route. Note it does not check availability. While *A RTW in economy books into fairly high booking class, there is not guaranteed availability especially booking at short notice.
Once you have an itinerary the tool will give you prices excl taxes & surcharges. You have the option of using the tool to send the draft to an airline for them to validate & price.
*A RTWs are distance based, with 29,000 miles or 34,000 miles or 39,000 miles. So if you are just over a threshold you may want to rework (if possible) to get under the threshold and save some money.
*A RTWs in economy must be ticketed at least 24 hours prior to departure of the first flight, so you'll need to get moving. I assume you meet the other requirements (minimum 10 days, minimum 3 stopovers of more than 24 hours).