Hi. The U. of Minnesota has a nice summary of trellis considerations here, and this page from the U. of Wisconsin is also good. One important consideration is whether you will be taking them down each year. In general, that is recommended because it decreases wear and tear (since they aren’t exposed to the elements beyond the growing season). That also allows you to move the trellises and rotate your crops each year. (If you aren’t familiar with crop rotation, I suggest reviewing this web page from the U. of Illinois; there is also a link at the bottom of the U. of Wisconsin trellis page.) Wood or bamboo trellises look nice and are natural products but don’t have the same material strength as metal, so you will generally need greater thicknesses for trellises made of those materials, though that also depends on the configuration of the metal (solid vs. a hollow tube). They also aren’t as resistant to the elements, so you would want to take them down each year if you can. I couldn’t find any studies comparing the effectiveness of different sizes or thicknesses of trellises, but my general advice would be to err on the side of a stronger trellis if your budget can accommodate it and to evaluate a sample in-person before you purchase a lot of them. If you are purchasing online, checking reviews can also be quite helpful. Regardless of the thickness of the trellis, spreading the weight over a larger area allows the trellis to support more weight, so cage-type trellises can be a good option. These can have a relatively thin main frame if it is solid metal (e.g., 7 mm); that may be equivalent to a 14 mm metal tube, though that also depends on the thickness of the wall of the tube. With so many variables, it is difficult to generalize about dimensions. I think if you were to purchase a heavy-duty trellis designed for cucumbers, you should be in good shape, since bitter melons are similar to very large cucumbers.