Bell peppers can be picked and eaten when they are green. They are also less perishable at this stage, which explains why they're cheaper and much more plentiful in a supermarket. Left on the plant, they become ripe---that is red--=and much more delicious, as well as more perishable and more expensive.

The freshest peppers will also have perky green stems that haven't gone wrinkly and brown yet. Here's a little article from Saveur a couple years ago (written by yours truly!) on choosing and handling hot peppers, but some of the principles are the same for sweeter ones: http://bit.ly/gfwuLW

I look for the peppers that have ripened to the deepest, richest color possible... that haven't yet started to get slightly wrinkly sections of skin. If you find those in that sweet spot they'll be plenty firm.

From the grocery store? I look for firm and shiny peppers, of the color they should be. Avoid wrinkled or soft peppers.