To decide which plants will do best on what kind of trellis, you need to narrow down its use.
If your trellis' primary goal is to be merely decorative, you won't need to train vegetables to increase your yield.
Arch and tripod trellises allow you to shape garden plants such as japonica or passionflower to build romantic outdoor spaces and craft topiaries from laurel and boxwood.
On the other hand, if you want your trellis to frame your outdoor space or screen a patio from view, you will need a plant that has a lot of leaves such as monstera or grapevines, or dense flowering plants such as climbing roses.
If you are placing the trellis outside a window, opt for a more fragrant plant, like jasmine, so the aroma drifts into the house. Fan trellises are excellent for flowering perennials, as the spread ribs at the top help show off blossoms to the best advantage.
Ladder trellises are excellent in vegetable gardens as the plants will climb up both sides, doubling your garden output. Tomatoes and nasturtium do exceptionally well on a ladder or A-frame trellis.