Normal climb speed would be 250kts up to FL100, then 270kts beyond that up to transition to Mach, where this becomes M0.73. The mode used for climb is normally FLCH, with power selected at CLM1.
Normal cruise would be 290kts, or M0.78, but selecting a long range cruise option can reduce these to as little as 250kts or M0.70 or lower. It all depends what the FMS calculates as the LRC speeds given the expected conditions on the day, and what speeds the crew elect to fly.
Normal descent speed is M0.76 or 290kts on transition, reducing to 250kts below FL100. In practice however, the normal descent profile is to use FPA to select a 3 degree slope and let the autothrottle control the speed. If the a/c is unable to maintain the selected speed, then just reduce the FPA as required. Using FLCH in the descent gives fairly high rates of descent and a steep deck angle, which is uncomfortable and not necessarily desirable.
All these speeds can be pre-selected in the FMS in the PERF INIT pages (page 1), and the flight conducted by selecting FMS speeds on the mode control panel on the glareshield, above FL100.
Standard approach speeds would be minimum 210kts 'clean' and also for holding, 190 kts flap1, 180kts flap2, 160kts flap3, (gear down) 140kts flap5 and Vap flap full.
190 kts would be normal for intercepting the final approach track, 180kts once established, and then the industry 'norm' of 160kts to 4 miles and the remainder in sequence after that, with the idea that final configurations and speeds are achieved by 1000' agl.
Hope you find this helpful. I know it's only a sim, but have fun flying her - she's a babe!