There are a myriad ways to cook vegetables, some of which are suitable for younger, more tender specimens, and some of which are suitable for older, more robust (one might even say tougher) examples.
The general principal (and there are a many exceptions) is that the older and tougher the vegetable, the longer you cook it.
I think your question indicates you already have the the start of the answer: if it isn't pleasant raw, cook it. And if it isn't pleasant when cooked briefly, cook it longer. Basically, the tougher and chewier (which often is directly related to how mature the vegetable is) the item, the longer it should be cooked.
Very young baby vegetables, and delicate leafy greens, young peas, and similar very tender vegetables are suitable for salads, or just being wilted on top of a hot dish without additional cooking.
Middle ground vegetables (these tend to be vegetables that you might eat raw on a crudite platter--they are substantial, but not tough) of hardier species like asparagus, as well as younger versions of hardy greens like kale, broccoli and so on benefit from a moderate cooking period such as roasting for 10-15 minutes, a brief saute, or a brief steam, but you may enjoy them with some of their original texture and snap left.
The sturdiest vegetables, and the most mature, such as mustard greens, older kale, mature cabbage, older Brussels sprouts, broccoli stems, and such benefit from long cooking which bring out their flavors and soften them. The long, slow cooked southern braised greens are an example. These vegetables can take the heat and retain their character.
It is difficult to give you a single rule, as their are a variety of treatments that will work in any given case.
Some cooking methods often come up, as they are optimal for the different rough categories:
I would suggest googling for recipes on the specific vegetables you have received, including their varietal name if you know it, and see what trends you get. Combining this with your growing intuition and experience should soon have you consistently creating vegetable dishes you enjoy.