There is a lot to think about when you go to design a trebuchet. Size, power, and look should all be considered.
However, the first decision that really should be made is just what object(s) you wish to launch. The nice thing about trebuchets is that they are capable of firing a good range of sizes and weights, if the trebuchet is of the proper size. Therefore, you can design around a range of sizes and weights, just don't make the ranges too large, especially the weight range. A trebuchet designed for launching tennis balls will also launch baseballs fairly well, but likely will not launch a bowling ball too well. At the same time, a trebuchet that is made for launching one pound rocks should have little trouble shooting a soccer ball.
Now that the size and weight of the future projectile(s) have been determined, the size of the trebuchet can begin to be determined. Ultimately, the size of the trebuchet needs to be limited by a couple of considerations. First of all, where will it be fired? If it is your backyard, then you don't need to worry about transporting it as much as if you will need to travel to a firing range. If traveling is necessary, or you wish to take your machine on the road for demonstrations or competitions, then you need to make sure that the trebuchet will not be too big to move with the vehicle you have available. If you have a trailer to build on, then you are limited only by the size of the trailer, but few people have this luxury. A sectioned frame is usually the best option for transportation inside of a vehicle. Still, such a frame can only be so big, since all of the sections still need to be transportable.
Another size consideration stems from a storage issue. If the trebuchet is to be stored outside in your backyard, then fine, just make sure that the neighbors will not have an issue with that, and make sure to weather-proof it well. Usually, a trebuchet will be stored inside, and so space becomes a major issue. Again, a sectioned frame can help, as it will take up far less space, but the space still needs to be there. Don't make a ten-foot tall machine to be stored in an area with an eight-foot ceiling.
And finally, just remember to built reasonably in scale for the intended projectile(s). Something only two or three feet tall will not work well for a bowling ball, and a ten-foot tall machine is not the best choice to launch baseballs, though both cases here will certainly be able to function. Also, make sure that the frames of the trebuchet will be far enough apart to allow the projectile(s) to pass through unimpeded.
Once scale has been determined, this more or less determines power, but this is still somewhat flexible. A larger counterweight is generally needed with a larger machine, since the arm mass is much greater. Generally, smaller machines do not benefit much from a heavy counterweight, but taller machines with longer arms do. At the same time, don't use a counterweight insanely more than your projectile weight. More about this will be discussed in a future counterweight section, but for now, just keep it sane. Make sure that whatever will be used for the counterweight will also fit through your planned frame separation with some room to spare.
Finally, what kind of look do you want for your trebuchet? If you merely want a trebuchet that will work well, looks may not be all that important to you. But if you are going for historical accuracy, then careful selection of materials and stains will be needed. Also, look at old historical drawings for an idea of what the frames looked like. Whatever you do, however, just please keep it safe!
Now, there is plenty of information that will be available here eventually that will pertain to all of the important parts of a trebuchet. While those pages are being built however, please feel free to take a look at Ripcord's website, as there is a fair amount of information there to start with. Then come back after the stuff is up here, it will cover plenty that Ripcord does not.
Information on designing a pouch is now available, though it is only for solid pouches at the moment. Net pouches will be included once we have tested more configurations of them.
Also, there is now information about material properties and how this might relate to a trebuchet design, specifically an axle. This is a prelude to a soon-to-come axle designing calculator.