Engines are manually run up before TO because fan engines have variable response to throttle movement. If you just engaged TOGA with the engines at idle, you are likely to end up with full power on one and the other still running up. You select a low-mid power to get the engines stabilised, and when TOGA comes in you get reliable response from there. Can't fully remember the 737-400 figure, but the 747-400 RB211 power setting is about 1 1/2" forward giving about 1.20 EPR (Engine Pressure Ratio- just a power number, nothing more precise) which I think it was for the 737.
TOGA is always used unless autothrottle is U/S. It gives reliable power settings without overboosting. I think it ends with the first thrust reduction after takeoff and becomes re-armed in the approach when the flaps move away from up or something like glideslope arm until touchdown or thereabouts.
If you're into simming, have you tried IL2? Been having the most amazing time Stuka bombing. What a sim. I find FS2002 typically MS clunky and disappointing.