The speed at which you’ll improve at the guitar depends on your goals. Why do you want to play guitar? What do you want to accomplish by playing guitar? How often can you commit to practice? How much money do you wish to spend on your playing?
A private teacher can teach you in a space of their own, or perhaps come to your home. He is often cheaper, but may not have the professional know-how or educational background of a music school teacher. He will surely be able to advise you on the purchase of the appropriate instrument or may even have rental instruments available. The private teacher is perhaps less the "teacher type" but rather the “mentor"-type. Often, private music tutors will be teaching guitar as a part-time job as they work through their musical education. Sheet music and other lesson materials are provided by the teachers themselves, and the lessons can be individually catered to the wants and needs of the student.
In a music school you will find professionally trained specialists for a variety of instruments. If your teacher is unavailable, one of his colleague could take over the lessons. If there are technical problems, such as a broken string, for example, replacement instruments and supplies are usually available on-site. Music school teachers can also help you in making a purchase of an instrument, and usually have good contacts within the local specialty store and with music venues. They may even organize concerts themselves. Furthermore, you’ll be around a group of other players, networking and meeting others with whom you may wish to start a musical project. Of course, this costs money, but music schools often offer rental instruments at a reasonable price, which can help you to stick to your budget. Music schools are more likely to require a several-lesson commitment, unlike a private tutor, which often operate as a sort of cohesive curriculum.
More detailed information about music schools in your area can be found through local associations. To the Verband deutscher Musikschulen e.V. (VdM) and to the Federal Association of German Private Music Schools e.V. (BDPM)
You’ll need to create and stick to a consistent practice plan in order to improve, and it is extremely helpful to have an experienced player at your side in the beginning to teach you the correct posture, fingering, and strumming techniques. Even if you plan on progressing on your own later, having just a bit of help in the beginning will go a long way.
Once you’ve conquered the basics, there are several ways to improve your playing quickly. There are guitar books with notes and without notes (only tabs), DVDs, and Youtube videos to learn from.
For example, we recommend the online guitar workshops from Guitar TV with Reinhold Pomaska and the million times proven guitar learning books by Peter Bursch.
Even as an adult, you’ll have fun and see your playing improve, even without being able to read sheet music.