I'm not with Laminar Research, just a fellow simmer in the UK :-)
Not being quite sure what your intended method of navigation is with the 737-800, but this is what I do to ensure that the aircraft follows the programmed flight plan.
1. Program the flight management computer (FMC) correctly with a valid route, obtained from Simbrief or similar
2. Initially set pilot/co-pilot HSI OBS & autopilot course to that of take off runway
3. Set autopilot airspeed to 140 knots, or as indicated by FMC
4. Set autopilot altitude to desired maximum flight level
5. Turn on flight director switches on pilot & co-pilot side
6. Turn on auto throttle switch on pilot side
7. Press LNAV & VNAV buttons so that they light up
8. Initially take off manually with 10 - 20 degree rate of climb, also manually following route on flight display map
9. Shortly after take off & wheels up, select autopilot engage CMD A button and the aircraft should then follow the flight plan programmed into the FMC.
Hope this helps