SO I have picked up playing the guitar. It has six strings and is a fretted musical instrument.
Are there any variants other than the six string version?
I think Keith Richards plays a 5 string guitar. I have been playing an electric guitar. The sounds is projected through an electrical amplifier.
Do you know when the guitar first gained popularity
There were many different types that preceded the guitar. There was the vihuela, gittern, four-course Renaissance guitar, and baroque guitar.
Are there any types of music that the guitar is particularly popular in?
The guitar is hugely popular with modern rock music. The guitar is played by using your fingers to pluck the strings. 
Are there any other instruments that compliment it well?
Sure. Drums and bass go well. Popular guitars are the steel-string, classical, and the archtop. 
It seems like the guitar has developed a lot over the years.
Different cultures have helped develop the guitar.  The string vibrations help the acoustic guitar produce different tones.