I believe that everyone is different, and should be encouraged to follow their own musical desires and interests. Here are some examples of different types of approaches to learning and topics of study.
The main types of guitar that I teach are:
The acoustic steel string guitar has been used in many styles of popular music including folk, pop, rock, blues, ragtime, country and western, bluegrass, etc. This type of guitar is played frequently with both plectrum (flat pick) and fingerstyle ("finger picking") techniques.
Electric guitars come in many styles and flavors, ranging from the hollow and semi-hollow bodied guitars used primarily in jazz and some blues music to the solid bodies favored by many rock players. The sounds of these guitars are produced with the aid of electronics, and are therefore ripe for many types of electronic sound manipulation such as effects boxes, overdriven amplifiers, etc. Most electric guitar players use a pick.
The classical guitar is a nylon string guitar. Classical guitars tend to have a beautiful sound which is more mellow than their steel-string cousins. Some people think of them as "Spanish" guitars. They are very close relatives of flamenco guitars. They generally have wider, flatter fretboards and slightly smaller, more rounded bodies than the average steel-string guitar.
Now here are some examples of areas of study:
Almost everyone needs to give some attention to learning efficient guitar technique. Your technique is simply the way you use your physical body to produce the sounds on your instrument. This "use" of yourself can be fluent, natural, and graceful, in which case it will serve you well, or it can be otherwise, in which case you will eventually run into difficulties. Learning good technique is a process of removing the obstacles that are keeping you from expressing the music in a fluent, natural, and graceful manner.
Everybody likes to learn songs. Some of my students like to focus almost exclusively on learning songs, while for others songs are just a part of a more comprehensive approach. Like I said, everyone is different; there is no "right" way. I enjoy helping people learn to play their favorite songs. Sometimes they've tried to learn from an online tab or video, but feel they need some one on one assistance. For classical students, they first learn short pieces composed specifically for learning purposes, then they gradually move into the repertoire.
This should probably be number 1 on the list. Deepening your sense of rhythm is perhaps the most important and impactful process that you can undertake while learning the guitar. Feel that groove!
This is something that some students are interested in learning, while others are not. I think it is a helpful skill to have, but I never force or impose it on anyone. For those who do want to work on music reading, I have some books that I usually use for the purpose. They introduce just a few notes at a time, so that the student can learn in easily digestible increments in a progressive, step-by-step manner.
This is something that I particularly love to teach. You better be careful what questions you ask me or you may not be able to make me shut up! Just kidding. But seriously, I myself have a passion for understanding "what makes music tick," and I like to share this passion with my students. You may want to see my gTheory pages for more information. Once again, though, I realize that not everyone is interested in understanding music. Some people just want to play it, not think about it. So, although I think that understanding music can greatly increase the enjoyment of music as well as stimulate the musical intuition, I try never to impose this understanding on those who aren't interested. Some people don't become interested until after they've played a while and get more serious.
Improvising is one of the things I truly enjoy about music. I try to get people started on improvisation early on in their musical training. It really is a lot of fun, and it helps you develop your musical ear and intuition at the same time! It is also a lifelong learning process. Those interested in Jazz music will be particularly interested in some of the ways that I combine Theory and Improvisation. Give me a call, jazz cats - I can turn you on to some heavy stuff!
Well, I hope that gives you an idea of some of the things you can learn in guitar lessons. Don't hesitate to contact me with questions or for more information.