I reall like the current colors and your red roof. I think you can change the house colors and not change the fence color. Here is one example that is in a tan family: With a white trim and dark brown shutters, I think it would work. Here is another example of a tan shade: I also like this light grey with white trim: Would you consider a green base: Then chose either a brown or red for the shutter.

All the suggestions above are perfectly good. However, when you have a house that is entirely painted, the options are so endless that it's easy to get stuck. I'd advise either finding photos of comparable homes in colors that you really love, and reproducing a similar palette on your home… or upload a picture of your house to a colorizing site, and play around with various combos. Sherwin Williams has a Color Visualizer that is decent. I don't mind a white house, but feel that the black trim is a bit harsh. On the railing especially- it feels like it is outlining itself too much. Reduce the contrast between the body and the rail and it will enhance the house rather than overwhelm it. You have a lot of choices, so just experiment and go with what resonates with you.

I love a QUALITY paint job. Few people know the ins and outs of a quality paint job but, a seasoned painter for INTERIORS will have many techniques and processes to dial up the end result. I love my painter and I listen closely to his advice and he is so expert (40 years) and good that he makes it look effortless. BUT IT'S NOT. Will find and post favorite picture of painted trim here. I think the secret is style and proportion of trim and then the quality of the finishing. Did you know most paint curing really needs 2 to 3 weeks to set up as a really good tough finish? "In a hurry" is the curse we mostly experience for improving interiors. I wonder sometimes how different things would be if people took the right amount of time to do things in the time frame related to that finishing task!

I don't know how hot it gets in Auckland in summer (I've only ever been to NZ in winter!) but if it gets hot, then go for a pale colour. Dark roofs should be kept for cold places!