I think that hunter green and navy blue looks great on chestnuts.
I like havana brown (dark brown) leather tack and leather halters.
I like white boots on chestnuts, especially if they have white socks and/or stockings. Polo wraps, in white, hunter green or navy blue. Saddle pads in hunter green or navy blue or white with hunter or navy trim. White sheepskin half pad, if needed.
I think that the navy blue with red accents colour choice you mentioned would look really nice as well.
Have fun shopping for your new horse!