Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Utah to Moscow as you normally would.
When deciding which route to take from Utah to Moscow consider Salt Lake City - Moscow Sheremetyevo, Salt Lake City - Moscow Domodedovo or Salt Lake City - Moscow Vnukovo as they are the most popular.
These are just IATA (International Air Transport Association) codes. They are used in aviation to identify and differentiate airports. That’s why a Salt Lake City Airport to Moscow Vnukovo Airport flight would often be abbreviated as a SLC to VKO flight. Moscow Domodedovo Airport (DME), Moscow Sheremetyevo Airport (SVO), Moscow Zhukovsky Airport (ZIA) are other airports near this flight route and their unique identifiers/IATA codes.