Styles throughout the Ages
The style of baseball uniforms has not been consistent through the ages. Looking at old pictures of players, you can see that players used to wear baggy pants tucked into high socks, and loose shirts with long sleeves. These were presumably made of cotton. Hats in this era were small with tiny cap bills... In today's game, you can see these old-style uniforms during Heritage Days, where some teams wear throwbacks to old teams.
Today's uniforms are made of polyester and much less baggy than their old-school counterparts. The hats are also larger and have larger bills.
Numbers on the backs of uniforms for purposes of identification were not added until the 1920's. Players were issued numbers that corresponded to their place in the batting order, Babe Ruth wore number 3, Lou Gehrig number 4, being an example of this.
For a good history of baseball uniforms, see the Hall of Fame site.