Texas Two-Step / Country Two-Step
The country two-step, often called the "Texas two-step" or simply the "two-step," is usually danced to country music and is extremely popular throughout the country.
This Two-Step is a dance with roots in European and Mexican dance history and appeared in Germany and Hungary in the 1800s. Similar steps danced at Mexican fandangos were also an influence.
As with other country/western dances, there are several different versions of two step. Even the same dance may go by different names depending on the area of the U.S., and even in the particular dance hall. There may be no one "correct" way to do a particular dance.
"A Better Man" by Clint Black or "A Few Good Rides Away" by Brooks & Dunn are good choices for Two-Step dancing.
Country waltz provides a great deal of freedom of movement that includes the other forms of waltz but is danced to a slower tempo than Viennese Waltz. Most of the movements in American Waltz can be done in country western waltz. The main difference is the music, which is logically country, and maybe cowboy boots and a Stetson hat.
Try "Allegheny Moon" by Anne Murray or "All in My Heart" by John Michael Montgomery for music to glide across the floor to.
A line dance is a choreographed dance with a repeated sequence of steps in which a group of people dance in one or more lines or rows without regard for the gender of the individuals, all facing either each other or in the same direction, and executing the steps at the same time. Line dancers are not in physical contact with each other. Older "line dances" have lines in which the dancers face each other, or the "line" is a circle, or all dancers in the "line" follow a leader around the dance floor; while holding the hand of the dancers beside them.