Are M16A2s with attached scopes common Designated Marksman weapons? If not, which weapons are most widelyused?

Marine designated marksman use a modified M-14

Actually, the army uses the M-4 rifle now, Marines use the M-16A2. The M-4 is a weapons system, it has a rail system on it for attachment of scopes and other cool gadgets.

when I was in the 82nd we each had a "quick shot" scope that you could hit up to about 50 meters, along with other goodies that made it possible to hit anything in any weather conditions

As a squad leader in the 101st, I had a German made scope on my weapon that I had zeroed out to 600 meters

Basically in the army, it will depend on what is called your units "TOE" (Table of organization and equipment) also, how much money your unit gets, and believe me, all units are not created equal. some units like Ranger Battalions get lots of cool stuff to hurt bad guys with. then on the bottom rung, you have the National Guard units that have to get leftover old army stuff (some of them still have M-16A1's)

Each branch of the service is different, as are different countries, but the most common sniper rifle in the US is some variation of the Remington Model 700.