Someone mentioned HOAs - allowed colors should be the first consideration (you agreed to follow those rules when you bought).
Also, certain styles of homes have traditional color palettes - it would be wise to at least consider those. They are traditional for a reason. If there is brick or stone, consider that - stay with coordinating colors. Same with roof color unless you plan to re-roof. Our neighborhood is mostly Williamsburg center-hall colonials. My colors are red brick in some areas medium gray siding, cherry red shutters/front door, white trim and an architectural shingle that is mostly shades of gray but some red. Neighbor on one side is a brown brick, tan siding, off-white trim and dark green shutters/doors, brown shingles.
I would also consider neighboring houses - don't want to match them but don't want to stick out like a sore thumb either (maybe that's just me - some people seem to want to stick out!).
Also, certain styles of homes have traditional color palettes - it would be wise to at least consider those. They are traditional for a reason. If there is brick or stone, consider that - stay with coordinating colors. Same with roof color unless you plan to re-roof. Our neighborhood is mostly Williamsburg center-hall colonials. My colors are red brick in some areas medium gray siding, cherry red shutters/front door, white trim and an architectural shingle that is mostly shades of gray but some red. Neighbor on one side is a brown brick, tan siding, off-white trim and dark green shutters/doors, brown shingles.
I would also consider neighboring houses - don't want to match them but don't want to stick out like a sore thumb either (maybe that's just me - some people seem to want to stick out!).