I'd also like to know was it more common to have large open field battles like you would see in Braveheart, or were prolonged sieges more common
I'm not an expert in this area, but this thread has some information relevant to you. You might also want to search this sub for chevauchée, which was the term by which such raids were known during the 100 Year's War. The TL;DR seems to be: Taking castles is hard, killing peasants and burning villages is easy, and if you do enough of the latter you may threaten the local lord's income/prestige enough that he has to come out and fight lest his vassals starve to death come winter and/or they surrender to you.