As a newcomer to the 777 from the 738, go arounds require a slight mental reprogramming as in manual flight, there is no pitch/thrust couple to ease the rotation to the go around attitude. Instead of a slight aft movement then a check forward to counteract the thrust coming on, a firm positive rotation is required to the new attitude.
Automatic go around is available on the 777 whenever the AP is engaged. With the AT armed (which it should be at all times even if disconnected using the push buttons) pushing TOGA will get you autothrottle and FD activation. If the FDs are off, the bars will disappear at ALT capture.
Sleeve of wizard - does the AMM tell you at exactly what point the TOGA switches are disarmed? Or does anyone have any earlier FCOMs/FCTMs which might contain more technical info than the current bunch?