There are many styles you might wish to explore as you gain expertise. Ethnic music, for example, encompasses as many styles as there are regions throughout the world.
Playing "Classical" music is a salute to the person who wrote it - the composer. You are trying to play his/her music the way he/she wanted it to sound. You will be directed, via "expression" marks and symbols, to produce your notes exactly as the composer heard them in his/her own head. You are, in short, the composer's actual instrument.
I very much enjoy the strict disciplines involved in playing classical music. Not everyone does. But the canvas is very much broader today than it was when I was learning my trade. Back then we had Mozart, Brahms, Debussy et al. Today we also have John Williams, James Horner, John Barry, Randy Newman and half a hundred others. All of them producing beautiful and moving film scores in the classical genre. So there is more to play, more to immerse ourselves in.
Today you can buy a book with a CD and play along with the best of them. It's an exciting time to be playing classical music.
Jazz improvisation can be an uplifting experience. I have earned a very good living playing all kinds of music, and I have enjoyed most of it. (Check out the "MyMusic" page.) But when it comes to sheer, unadulterated fulfilment, jazz improv takes the cake!
Like most, improvisation used to be a mystery to me. And the questions are universal. What is it? What are they playing? And, possibly the more pertinent: Where is it coming from? This latter question is the most important one, and the hardest to answer.
Way back in my formative years I saw an interview with the late Charlie Parker, who was asked that very question. His answer puzzled me for a long time. Short and to-the-point, he said, "The answer is in your front room!" I didn't get it. Not then. I know now that he meant that you have to listen to it to be able to play it.
A silly example... QUESTION: "Where can I buy a plattenarbor?" ANSWER: "You'd better tell me what a plattenarbor is first!"
But don't dwell on it. You can learn to improvise, and very easily - dependent, of course, upon the level you wish to achieve. I can tell you that the better you become, the better you will want to be. In short, Improvision is your own version, made up on the spot, of someone else's melody. That is a generalisation, but it's accurate. On the other hand, you don't even need the original melody.
Just pick up your instrument and blow something, anything. You are improvising. The only question might be, does anyone else want to hear the sounds you are making? That question leads on to a whole host of other questions that, for the moment, are best left unasked. So, dip your toes into the lake of improvisation and see where it leads you. You'll be out there up to your armpits before you realise it!.
Graded exams can be measures of a student's progress, supplying the individual with periodic, achievable goals. Something to shoot for It does have to be remembered, however, that in many areas of both formal and informal education it is entirely possible for a student to pass a series of exams, whilst not actually progressing in overall musical ability. In other words, they study for the exam, and not for the actual skills involved. I avoid this syndrome wherever possible My students would not be advised to put in for a grade if they were not actually at - or beyond - the required level. For me, the end result is the ability to play music, not (necessarily) the simple possession of a piece of paper.
My approach is flexible and dynamic, tailoring the practice requirements to the individual students' needs and abilities. The whole process should be enjoyable and rewarding. And the student must know that the actual grade certificate had been well-earned. There are several bodies that conduct musical grade exams. I favour the ABRSM. THIS link takes you to their web site.