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Container size matters less than people think - drainage and sun exposure are actually the bigger deal.
That said, I'd go with at least 5 gallons (roughly 20 liters) per plant; smaller pots dry out too fast in summer heat and stress the roots. If you're on a balcony with decent sun and airflow, you can push it to 10 gallons and give yourself way more margin for error with watering.
The main thing is making sure there's a drainage hole, because peppers hate sitting in wet soil.
Drainage holes matter way more than the exact size, but I'd actually lean toward bigger rather than smaller - I've seen people struggle with 5-gallon pots drying out too fast on hot balconies, especially if you're dealing with afternoon sun.
Go with 10 gallons or more if you can fit it, and make sure whatever you choose has multiple drainage holes on the bottom. Peppers are pretty forgiving about being slightly rootbound, but they hate sitting in wet soil, so the extra volume gives you a bigger margin for error when you're watering.
Growing peppers in pots on a balcony is definitely doable, though the heat reflection off walls and railings can actually work in your favor during the growing season. One thing that doesn't get mentioned much: wind exposure matters a ton on balconies because it accelerates water loss from the soil, so you might need to water more frequently than someone with the same pot size on ground level. If your balcony gets baked by afternoon sun, consider going a bit larger (7 - 10 gallons) just to give the soil more thermal mass and buffer against those dry spells between waterings.
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