Pots, unsually the bigger the better for most anything. Plants can get cramped roots in smaller pots and then the plant gets stunted, or need more frequent waterings. The bigger the better, unless you're only growing from seeds and will be transplanting. Dill doesn't transplant well.

You need to do some research about the mature size of your plants. For instance, rosemary can get very large - mine gets to well over 1.5 metres (that's more than 4ft in your language)and about the same width. With most plants, if you think of the root system being at least as wide and deep as the top bits - that'll give you a rough idea of the size of pot that's needed. That's in theory. In practice, you can use a slightly smaller pot, because potted plants rarely reach their optimum size in pots - they'll always be stunted to some degree. But still, you need to allow those roots room to spread and not become scrunched.

As for mint - well, there are umpteen threads here about how far down it can grow, and how far it can spread. A pot about the size of your olympic swimming pool will contain it for a short while..... It's one of those plants you will need to keep re-potting and dividing to keep it under control. It has a very aggressive root system, and propagates itself by every means known to mankind!!

Any plant which has a tap root will resent being transplanted. That includes parsley, so repot it early, before its taproot is fully established. A mature Italian parsley is bigger than what would comfortably fit into your oven, but the root system tends to go deep rather than wide, so you need a pot which allows for that.

Yes, when it comes to pots, size DOES matter! The bits underground are a plant's source of life - unless they are healthy, the plant will die. If the roots can't grow and spread to accommodate the needs of the above-ground bits, it will never survive. When a plant is pot-bound, the roots get scrunched and stunted, and for the plant, it's like trying to drink through a bent straw. Can't be done. And if there are more roots than soil - where are its nutrients going to come from? Or its support?