Pruning is an interesting topic....and potentially contentious, lol.
I have tried both. I find that when I am growing on land, I prefer to just leave them grow. My yields are perfectly fine (but you do need a good staking procedure!). But, in the containers, I do like to prune most suckers. I leave maybe two main stems (not one) and it works out well. If you prune too much, you can get sunscald...and they look naked! I like it when the branches are willy nilly - they look so robust! But, in a container, too many branches can be daunting.
Per the peppers, I think you'll get varied answers. It doesn't matter when you remove it as long as it's gone before it gets pollinated and produces fruit. Some people say that if you don't remove it, the plant will put it's efforts into producing fruit, and not into growing. Others say that if you have fertilized well, this doesn't happen. One argument I read said that you pinch all blossoms until the plant is as tall as it's supposed to be. Another argument is that if the plant is stressed, remove blossoms, but if it's not, leave them....(yep, it's like the tomato sucker debate...)
If it's cold, like it has been, the plant may drop the first blossoms anyway, so no decision needs to be made! I wonder if it would help to put row covers on these plants that love the heat during cold spells like this. (My okra is very unhappy....)