Of course it isn't news to anyone around here that I'm very picky.
I don't eat summer squash, at least not cooked. That's a different animal altogether. I'll put some zucchini in a salad. But to me, squash is that deep orange pile of richly flavored, smooth textured mashed potato substitute.
After years of experimenting, I still goof up on occasion, but this is how I pick a good squash (I use only acorn or buttercup):
First, don't even look at light green, it's just not ripe. You want dark green or mottled (which I think is riper), and second, look for a bright orange spot on one side. Why that spot should make a difference I don't know, but it does. Another thing I look for is being relatively light, because I prefer it on the dry side rather than wet. If it's heavy, it's full of water. If you can get them from the farmer, I think you have a better chance because, like everything else, supermarket squash tends to be underripe.
If anyone has other clues, please feel free to enlighten me.
For cooking it ... I've heard all kinds of things. Some people cut it in half and put it cut side down on a tray in the oven. Some people cut it up and boil it.
All of that is waaay too much work for me. I just put it whole in the microwave (on a plate - it gets messy) for 20 to 30 minutes depending on it's size. If you can pull the stem off easily, it's done. Cut it in half, scoop out the seeds and then the flesh. Mash with butter. Love it.