Material for external insulation

I plan to insulate a wall from the outside. The wall is 36.4 cm thick plus plaster on both sides. Material of the bricks... hard to say, they are gray and when broken are something like black gravel (approximately). The effort should be reasonably limited. That means I don’t want to have to remove old plaster and the like first. More or less directly on top, and that should be fine. The material should rather improve sound insulation and not worsen it, at most remain the same. A wooden facade is planned as the new finish, I’m not exactly sure how and what yet, but definitely wood and no plaster. Of course with an appropriate coating. The wall is occasionally strongly exposed (east side), the weather side is the west side. Moisture should therefore also be able to escape well again? How thick should outer insulation be applied? Is 5 cm of insulation okay, the lower limit or even the upper limit where cost-benefit is still justified? The effect of the insulation should definitely be noticeable and not just theoretical. I don’t want to spend a fortune, but since there aren’t that many square meters to insulate, it can also be a bit more expensive if it really pays off. The area to be insulated is about 30 m². Is it still possible to carry this out before winter? Let’s say mid-November? Does it have to be dry on the day(s) of installation? If the wall is wet I obviously would not want to apply anything.