Usually they start out green, then change directly to one of those colors -- red, yellow or orange. green is immature/unripe.
But some varieties take a long time to fully ripen, so there are varieties that ripen more quickly.
Grocery store peppers tend to be hybrids. If you get an open pollinated variety, then you can save seeds from the ripe peppers. However, often hybrids are more productive, change colors all at once, etc. have traits that are convenient for market growers.
There are other kinds of varieties too -- sweet but not bell shaped. Then there are peppers that start out green and turn purple, ones that start out purple then turn red, etc. (these are not necessarily sweet peppers.)
Depending on where you live, you may want varieties that ripen very early.
Another issue is not all fully ripe/colored peppers are really sweet. I just had a yellow long pointy Doux Long d'Antibes for lunch and was blown away by the sweetness and juicy thick walls.
The I had an unidentified green one that I thought was horrible -- thin, tough, and tasteless. I'll need to pay more attention and never pick that one as a green pepper.
For early maturing red bell pepper, I'm trying King of the North this year, but Donkey Ears -- and Peperone di Senise, two other not bell-shaped sweet red when ripe peppers have been earlier.