Hello Matt,
the first thing is to see if there are any problems with your existing system. The easiest way, if you have a meter, is to measure the voltage drop at the headlights themselves. (Light output is very related to applied voltage). If there is a significant drop then you need to find out where that is. (Pay particular attention to the earth).
Until that is verified, a larger alternator will not make any difference and halogen lamps, although brighter, will not give their full output.
When you satisfied that all the voltage available is getting to the light unit then the easiest upgrade is halogen lamps of the same wattage (Assuming you have sealed beam lamps at present). This will not increase the load on the wiring at all but does give much better lighting. Personally, I am not in favour of very high powered lights for road use as they are more dazzling for other road users especially in the rain.
A properly designed relay system will help in giving a slightly higher voltage to the lamps (giving a better light output) and reduce the load on the switchgear.
An alternator upgrade is only necessary if you find that your existing alternator cannot keep up with the load you have. Dimming of the lights at idle is not a issue, in my view, unless you find it affects your indicators significantly.
Alec