The first thing that you should consider is what kinds of opportunities are open to you. Finding the right situation with the right support and the right audience is something that you want to consider. Take some time and really consider what your options are going to be when you are thinking about what sort of place is going to suit you best. There are many different venues open for people who have received their doctorate and finding the right place is something you need to think about.
Obviously, pursuing a more extensive education for a career in academia is greatly encouraged. If you feel that you still want to refine your research skills and want to make sure that you are offering the kind of broadness in experience that may be expected, a postdoctoral fellowship may be the way to do it. Particularly if you are interested in working in the sciences, a change of scene as far as a lab goes, or even going to work overseas, this option can make a big difference. Take some time and make sure that you consider what needs to be done when you are looking at getting a job in academia. When you are looking forward to an activity like this, keep in mind the fact that the more publications you have the better off you are going to be. Really consider what is on the table when you are thinking about getting into academia.
Working in academia has many advantages that you may not have initially considered. In the first place, you will soon realize that you are in a place where you can broaden your experience, making sure you are well rounded if you choose to leave academia, and you will also find a postdoctoral fellowship can help you figure out whether you want to stay in academia permanently. Do keep in mind that for the most part, being able to continue in a postdoctoral position like this is fairly rare. These positions also tend to be fairly limited-term engagements. Finding a position of this sort on a permanent or rolling basis is quite rare.
If you are interested in leaving academia, at least for a while, you will find that it is time for you to consider what is available when it comes to research institutes. Many people who are in their postdoctorate phase will find a place in research institutes. This is a good place to be if you want to be in an academic environment without needing to worry about undergraduate teaching duties. You will tend to be funded on a short-term contract and this is a good place for people who have more experience in research to eventually find a permanent post. This is somewhat comparable to a senior lectureship at a university.
There are plenty of places available when it comes to industry, especially if you work in the science fields. Remember that the world you are considering is results driven and can be highly stressful. You also may have to travel. You may face management or may even run a lab yourself, depending on what area you are considering. There are many different things that you can do when you are looking at moving forward.
There are many different things that you can do when you are looking forward to your postdoctoral career, and as you are doing them, the most important thing for you to do is to figure out what you really want. What will make you happy? Where do you see yourself in the next few years? This is an important juncture in your life and it can cast a shadow over what you are looking to do in the future. Take some time and make sure that you consider what your options are and where you want to take your work. What sort of research do you want to do, and where do you see your research taking you?