Hematite α-Fe2O3
Colors: Red range (purple, pink, black, orange)

Goethite α-FeOOH
Colors: Brownish-yellow range (yellowish-green (small particles) to yellow-browns (large particles) )

Limonite FeO⋅OH + FexOx
Colors: Yellowish-red range (composite mixtures)

Lepidocrocite 𝛾-FeO⋅OH
Colors: Brownish range

Maghemite γ-Fe2 O3
Colors: Brown-reddish range (dark red, black-brown-red)

Magnetite Fe3 O4
Colors: Black range (Black, dark red, black- brown)

Vivianite Fe2+3(PO4)2 . 8H2O  (iron-phosphate)
Colors: white, blue, blue-green, green, black

Siderite FeCO3 (iron-carbonate)
Colors: Brownish-orange, Brownish-red, Brownish-yellow

Basic color change info:
There are five rudimentary ways to change iron-based colors: temperature, oxygen, light, water and weathering. Exposure or admixtures with other elements also change the way we experience the color of iron-based minerals.

You can also force transformation of color with the following:
Oxide dehydration (removing water)
Oxide hydration (adding water)
Intervalence charge transfer (exciting ions)

To learn more in depth, a great iron-oxide laboratory resource is:
Iron Oxides From Nature to Applications edited by Damien Faivre.

For pigment foragers and natural paint makers:
Colors From the Earth by Anne Wall Thomas (thought out of print) is the classic text.