You have to master country guitar basics first if you want to master country guitar. It's that simple. The fundamentals always come first. It's crucial that you understand the sound, style, and gear involved in getting the perfect country guitar sound.
Country guitar is known for its "twangy" sound, a tone usually associated with the Fender Telecaster, a guitar born in the 1950s and that came to be almost synonymous with the sound of country lead guitar. Everyone from Brent Mason to Brad Paisley to Danny Gatton has favored the bright twang of the Fender Telecaster at one time or another. While country guitar is generally associated with a bright, clean tone, the fusion of country, rock, and pop styles over the past twenty years especially means that you will find country guitar players who have sounds that often rival that of rock players.
Of course, we shouldn't leave out the acoustic guitar as a significant component of the country guitar sound. Popular acoustic guitars with country players include Takamine, Taylor, and of course, Martin.
In addition to the "cowboy chord" rhythm style that is so prevalent amongst country rhythm players, country electric players use a wide variety of electric-specific techniques that help define the sound of country guitar. One of the most popular techniques is a pedal steel emulation where one plays a double stop (two notes), bending one note while another remains stationary.
"Regular" double-stops are also very popular in country guitar, as are hammer-ons, pull-offs, and slides. These are techniques that are used in other styles as well, but when used by a knowledgable country player, they help define country tones. Perhaps one of the most notable country techniques is known as "chicken picking," where one combines fast right hand picking with staccato and muting techniques. Hybrid picking is also a common component of "chicken picking" and country guitar in general.
As mentioned previously, there are some guitars that are nearly synonymous with country guitar, the Fender Telecaster being the primary electric guitar. Of course, many players have used other instruments with no complaints. Clint Strong used a Gibson Les Paul Custom when he played with Merle Haggard, and you never heard anyone say that Clint didn't sound like a real country players. And before the invention of the Telecaster, Gibson guitars ruled the day in country music. Chet Atkins made a name for himself using primarily dual pickup Gretsch guitars. Still, the Fender Telecaster is a good place to begin.
As far as amps are concerned, you generally want to have a clean, non-distorted tone so that your chicking picking licks come through loud and clear. That said, there are many country players today who use overdrive as an integral part of their sounds.
Regarding effects, most country players will also use a fair amount of compression, delay, and, of course, reverb. A volume pedal is standard equipment to achieve those violin-like swells and like I mentioned above, you'll find many country players who use many different types of overdrive pedals. Not a whole lot of heavy metal type distortion, but heavy overdrive is not uncommon these days.