There are some nice-looking combos here:

https://thecolorconcierge.com/best-exterior-paint-colors-red-brick-homes/

I love the retro diamond design on the side, I hope you keep them. :)

Your neighbor's siding is a medium blue-gray. If you used a lighter gray with less blue you would coordinate, but still look different. Look at Repose Gray and Crushed Ice. Test the color on a board, outside, and look at it next to your neighbor's siding. I know you don't want to copy them, but if your color clashes it will make everyone who goes down the street wince. I don't know that I would use white on the trim. The white of your garage door doesn't look great with the brick - it looks too stark. Once you choose your main color, use a lighter or darker version of it for your trim.

“Look at Repose Gray and Crushed Ice.”

Do check those colors. Repose Gray is a warm gray and will look fairly light on the exterior. It should pair well with the brick and also with your neighbor’s blue-gray. Whatever you choose, the garage door should be the same color.

White, to unify the garage door with the whole look.

Anything dark will fade and the intense sunlight peels over time. the garage door is factory, right?

I like Beverly's ideas above. I'd also take a look at a dark sage green and make sure the side of the house is all one color.

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The taupe of neighbor's garage door on siding and garage door would complement your brick and neighbor's blue house. Leave reddish trim you have.

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