Pepper seeds begin to mature when the pod turns color. Green peppers are immature peppers and the seeds are not viable. Red or yellow, the seeds may be viable.
The largest issue with using store bought fruit is the seeds need to be treated with TSP (Trisodium phosphate) when they are harvested. This treatment kills tobacco mosaic virus. TMV and other tobamovisues are common in production areas.
The plants will also be a segregating F2 plant. So the fruit/plant will look a little different from the parent (F1). Not a big deal in my opinion.