Since the New York Football Giants’ inception in 1925, the team’s colors have always been red, white, and blue, sometimes with grey used as an accent color.
Despite the Giants’ nickname as “Big Blue”, the team actually sported red jerseys for some of their home games prior to 1953, alternating with their now famous blue jersey. For home games, they also sported blue helmets, white tight pants, red socks, and black cleats.
In 1954, the NFL pushed franchises to wear only one color for home games.I found some more information here. This influenced the Giants to choose the blue jerseys as part of their official home uniform. The red jersey would not be worn again until 2004, when it became the Giants’ official alternate home jersey.
In the 1960s, the Giants experimented with various different types of striping on their home uniform pants. The home uniform’s biggest transformation came in 1975, when the blue jersey gained added white numbers with a red outline, and added red and white striped sleeves. The white pants added a blue belt and a new blue and red stripe pattern.
Presently, the Giants sports a simple style of home uniforms: matching blue jerseys and gray pants paired with blue socks.