This can be somewhat of a controversial topic among pyrographic artists; they all have varying opinions on which burners are best. Although I will tell you what I like and why, I will try to be objective in my reviews. For most burners, burner and tip preference becomes what works with your style, and what you become used to using.
Solid Tip (single temperature) Burners:

The solid tip burners are the best place to start; it will help you get a feel for burning and learning the skills that you need. They are the least expensive, and even most advanced burners still use them from time to time for certain projects and effects that they are better suited for than the other types of burners. I have seen some incredible work from Pyrographers who have done it all with an inexpensive solid tip burner.
If you do use a solid tip burner, one problem you will have is “over burning” which we will discuss in better detail in the tutorial on burning. This is an effect caused by having the temperature set too high. The solid tip burners do not have a way for regulating temperature, so you must make your own. You can wire a standard dimmer switch in-line with the power cord to accomplish this. Others have made boxes that will plug into the wall that have the dimmer and a receptacle in the same box, the dimmer is used to control the voltage of the receptacle that you can plug your burning pen into. This is a good method for those who do not wish to alter the cord on the actual burning equipment, which will more than likely void any warranty if you do. I would recommend getting the help of a licensed electrician for this, you will find it a necessary control device for any solid tip burner.
Adjustable Temperature Burners:Most Pyrographers find that as they get more advanced they like to invest in an adjustable temperature burner. There are many advantages beyond the temperature control, which is something we showed can still be accomplished with a solid tip burner. The hand piece will heat up and cool down much quicker, and it is much smaller. Your hand is closer to the tip which gives you better control, and the smaller tips are capable of finer detail than you can get with most of the single temp tips. There are also a large variety of tips available for different effects and textures.
I personally don’t find any significant advantage to all the “bells and whistles” that you can get on the high end burners, the quality of the simple single port controller is as good as the others, and the tips are all the same, so unless you find that you are switching tips quite often, for the price, I would just go with the basic setup to start with. Also, the base unit I use is only 50 watts, one of the smallest units. I don’t think that I have ever set the dial above 6, and I find that it gets more than adequate heat in the tips.
Interchangeable tips:
As a once licensed journeyman electrician I can tell you that there is no way around the fact that if you are constantly replacing tips in the end of a hand piece, they will eventually loose their continuity. In other words the electrical connection will eventually get loose, it will not work as well, and then finally not at all. It is well worth the expense to buy the tips that are a solid hand piece.
Which tips?It has been my experience, with some exceptions, that most pyrographic artist’s do 90% of there work with one tip. Of course the preference as to what that favorite tip is varies from one artist to another. Generally speaking, you will want at least a skew, shader, and a writing nib. The next tip you would get is one of a variety of small detail tips for doing small intricate work. Each manufacturer depending on what burning system you use, will have a description of what each tip is used for in there catalogs if you should choose to add to your collection.
Rounded Skew, tip detail. Round Skew vs. Standard Skew