White is not a country shirt. White with tweed is the mark of a stooge, someone who knows only that white is “formal” and a tailored jacket is “formal” so they “go together.” White with brown cannot altogether be ruled out but it is not for n00bs.
White is almost never good with an odd jacket. Doc can talk all he wants about the 60s and he will not change my mind about this. For virtually any odd jacket combo you can think of, it's not just that a blue shirt would be better but that a white shirt is wrong. The only exception is a blazer and grays, worn at night. (A blazer and khakis--aka the "California Tux"-- demands a blue shirt.) A blazer and a white shirt in the daytime is not "wrong," but it's also never the best choice. A white shirt worn with a blazer should really be a button-down and should never have French cuffs.
White is thought to be the perfect background for a variety of ties, a "blank canvas." But this is not so. Many colors look absolutely terrible with white: yellow, orange, rust, lavender, purple, nearly all greens. Even red, a very common paring with white, always looks better on a blue background (not that you should be wearing true red ties) and burgundy or maroon looks better against pink.
So does work with white? Above all navy. Black. Gray. Silver. Combinations thereof. Certain very pale (I mean VERY pale, so pale it takes a second to recognize what they really are) golds and greens. Any shade of blue, especially the light blues which look best against white.
Suits should be blue or gray. Tan with white is an "advanced" look that can be good but let's leave that aside for now. Blue or gray. Dark suit, white shirt and dark tie is a great formal evening look. But if you are not going out, make the tie lighter than the suit. With a light suit and white shirt, wear a dark tie. Don’t wear a light suit, white shirt and light tie, or at least, be careful.
If the suit is gray, the tie should be blue. If the suit is blue, the tie should be in the gray black silver family or anyway one of the other colors. This is not ironclad it just looks a little better than blue on blue or gray on gray. Though, for a formal daytime event, gray suit white shirt and silvery tie is the best option. For an ultra-refined, but also very sedate look, try a blue suit, white shirt and black tie. This is best limited to night time.
Unless its pattern is of the wedding variety (checks and plaids), do not wear your wool ties with a white shirt.
White shirts nearly always demand black shoes. If it's a more casual outfit (blazer & white BD), mink suede is a decent substitute, since you should not be wearing black shoes with a blazer.