I mostly grow peppers in pots. The size pot you need depends a bit on what your limitation is, whether it be # of plants, # of pots, or sunshine.
For someone with a short growing season I would recommend a greater # of smaller pots IF you have to choose, because not only will the plants not get as large but also if you have 20 plants in a space where you'd otherwise have 10, for the first couple months they're catching almost twice as much sun in total. You end up with smaller plants and fewer peppers per but the larger # of plants makes up for that. However, towards the end of the season you may have to water and fertilize more often, especially if it's much above 85F towards the end of summer.
By smaller pots I mean 2 to 3 gallon filled nearly to the top. I wouldn't bother with anything smaller than that. 5 gallon could be considered a standard size that's common due to the # of 5 gallon buckets existing in the world, and just adequate for a medium length season of about 6 months from last frost to first frost if starting with nursery plants or sprouts started inside a month or two before the last frost of spring.
If they get a lot of sun and some fertilizer there are gains to be had from 10 gallon, even 20 gallon pots. The latter is particularly beneficial in hot areas where you cannot water more than once every day or two. I can only get my container grown peppers to be as large as counterparts in the ground if using pots 10 gallons or larger.
The main problem I see people having with container growing is their soil isn't fluffy enough, compacts too much, drains poorly, and causes root rot. The plant may still look ok but growth is stagnant, they may only get a few dozen peppers instead of hundreds. Of course this also depends on what size the peppers were supposed to be, hundreds of bells or other larger varieties would be an unusually healthy super-plant.
I find that my potted peppers almost always need staked, otherwise when a big gust of wind comes along the roots can't support it well in the fluffy soil.
Another issue is amending the soil. I reuse the same soil every year but keep adding composted yard waste including leaves, pine needles, wild grasses, spanish moss, coffee grounds, egg shells, small twigs, the shredded remains of last year's crop, etc. Just about anything brown but not a lot of fresh lawn grass clippings because too much at once seems to promote fungus.