Full-colour comics are only overwhelming if the artist hasn't been paying proper attention to their chosen colour-scheme!
@Kaykedrawsthings has already given solid advice, and I'll follow up on that.
Bright, primary colours might seem like a good idea at first, because they're intense and call for attention - but if you use ONLY bright, primary colours, the end-result is often an eye-searing mess. The eye tries to go everywhere at once, unable to pick which colour needs the most attention, and so the page looks busy and, well, loud, for lack of a better term.
The urge is certainly there to use primary colours, because, well, we all know that grass is green, right? And that water is blue, and so on.
Except that's not really the case. I mean, grass IS green, but can also be almost every other shade imaginable - dry, dead grass is yellow or brown, fresh and new grass is yellow-green, some species of grass are so dark green they're nearly blue, etc. Water isn't blue entirely on its own - it's mainly blue because it reflects the sky. If you head down to the seaside, you'll notice that sea-water can be a whole lot of different shades, from brown to bullet grey and every shade in-between.
Light matters a whole lot, as do the colour of the shadows. A bright, sunny day at noon looks different than an overcast day at 7am.
Cool colours - blues, greens and cold greys - give a different impression than warm colours - reds, yellows, oranges - so which temperature of colour you pick matters too.
Colouring is part science, part art, and it's tricky to get the hang of, but it's really fun to experiment with and I am deeply, deeply impressed by people who do it well.
It's time-consuming, to be sure, but speed is a matter of practise! A year ago, I was nowhere NEAR as fast in finishing a fully coloured page as I am right now. 
