I always started mine in small containers to protect them from the crows, then moved them to near my back fence.
If you want to keep them in containers, I think they would do better in something broader than a 5-gallon bucket, especially if they'll be exposed to any wind. Perhaps you could find some big plastic tubs at the Dollar Store, or on sale at Walmart. Just be sure to drill plenty of drain holes in the bottom, and don't use a heavy clay soil for planting the seedlings.
I would also make sure to grow them beside a trellis or tall fence, so you could tie the tall stems to the support as they grow. JMO opinion, and the way I would do things. I'm sure others will offer more ideas.
"Isn't it enough to see that a garden is beautiful without having to believe that there are fairies at the bottom of it too?" - Douglas Adams