One of the things that I ask a student when they first start is what kind of music they listen to and what they want to accomplish on their instrument. You should ask yourself the same questions. Most students start out with the same basic exercises and theory and get into specifics later. Most students just want to learn songs but I encourage them to learn theory along with some improvisation and writing skills. It helps with their playing, ear training, and takes away some of the mystery away from how music is created.
Once you see how songs are created and some of the theory behind them, playing your instrument and learning songs becomes a lot easier. For instance, once you learn about the different forms in music, it becomes easier to a) figure out what you're listening to b) identify where you are in the song, c) memorize the separate parts. Once you learn about some basic chord progressions, it becomes easier a) to play them (since you've gone over them so many times), b) to recognize them (guitar players can usually tell when a D or G chord is being played), and c) easier to improvise or write your own songs (since you know the progressions in advance). Once you learn the theory behind playing solos, it becomes easier to a) learn solos off of CD's, b) extend or improvise on a given solo, and of course c) make up you own solos.
What Are Ya Into?
Beyond just learning theory, you must try and learn things that apply to your genre of music. Learning music isn't hard but it takes time, You want to use that time learning about what applies to your style of music first. After you've been playing a while, you may want to get into different styles. For example, after a while some players get into learning more complicated chords and scales. If you're into country or rock, learning 13th chords won't be of much use to you. Learning these chords are great if you've been playing a while and are starting to get into more complicated stuff. But if you're struggling to get the basic chords together, learning these chords won't be of any use to you at all. The truth of the matter is that there is a world of learning with the basic chords and if you don't know how to use these properly, the more difficult chords aren't going to help.
If you're into country for example and want to learn how to pick like they do, you should spent most of your time on the basic major, minor and pentatonic theory. Also, except for some country swing, most country doesn't go beyond the basic triads (it does use 7ths on occasion). Country music likes to keep things simple; it uses these basic tools in a million of different ways. It's important that you know the basic theory behind the songs but them you have to get used to using those tools in many different ways. For example today's country uses rock scales and licks, major and minor scales, and some old school country & bluegrass idioms and chord progressions. That means not only learning songs, progressions and licks in country, but also some rock, pop and bluegrass. These all belong in today's country to varying degrees.
Rock music has a theory all it's own. It's mostly based upon blues theory (which the jury is still out on!), but also uses major and minor scales and in some cases (alternative, prog-rock) more extended harmonies and scales. Rock has been around a while, there are a lot of different styles so there are a couple of avenues to take here. You may want to start with some basic blues, some classic rock or come older metal. Within each of these you will see the roots of all of today's modern music. A lot of classic rock is based around the riff; a repeated figure that forms the basis of the harmony. Some classic rock uses variations of the 12 bar blues, while others will stick to the basic I IV V.
Just learning what a I IV V is isn't enough. You have to learn all of the various ways it's used. What chord does it start/end with? How many bars of each? What are the rhythms used most often? All music uses the basic I IV V, it's all about application.Older metal (70's) was also based around blues chord progressions but extended into the minor scale (and model harmony) and chord progressions based around that. Today's rock uses all of these (sometimes within the same song). Modern metal is an example of taking the theories and mashing them together; riffs, modes, esoteric scales and arpeggios.
If you think there is no theory behind modern rock/metal/dance/hip-hop, you're wrong. A soon as music becomes a style, there is a theory behind it. Theory is simply an attempt to explain what's happening and the tools that are typically used. The fact that the musicians don't have a name for a certain scale or chord used is irrelevant.Pop
Pop uses all of the above to varying degrees. Some pop uses rock idioms while some sticks to your basic major/minor harmonies. Like rock and country, there are many variations on the basic chords. A lot of the theory is used over and over again but you have to learn the basic progressions, rhythms and forms used. Guitarists and pianists will take the same chord progression but play them in different ways. There aren't as many solos but there are a lot of things to learn about putting together parts to make an interesting arrangement. That includes chord embellishments, fills and various accompaniment styles.
So Why Though?
You may be asking yourself that if some of these musicians who are making the music don't know the theory, why should I? In fact, they do know the theory. Jimi Hendrix knew the theory. James Hetfield knows the theory. I know what you're thinking; James has said numerous times that he doesn't know any music theory. But he knows where to go when he plays chords. He knows where to go when he plays a solo. The fact that he doesn't know the name of scale or chord doesn't mean he doesn't know the theory. It was the same for Jimi Hendrix who many thought didn't know any theory. After playing with the Isley Brothers for an extended period, he said that he had every one of those songs and progressions ingrained in his head. If you stick to a certain style and have a discernable sound, there is a theory behind it.
Mimick, Learn, Apply
The fact is that all musicians learn the same way; through mimicking, memorization and application. Jimi had tons of progressions and licks at his fingertips every time he played. This was from practicing and playing these things over a period of years. James Hetfield has a sound in his head. He then searches on his instrument until he hears that sound. If you're a fan of the music, you'll notice a lot of ideas and progression are used often. If your know the theory, you can create within that style with accuracy. The same ideas are used over and over, that's why the music is its own style in the first place. If you take the time to learn the theory, the style will come quicker to you. It'll be easier to hear what's going on, know how to play it, and ultimately write and play it until it's your own.