Hey!
For appeasement, I think the main debate is really whether Churchill was correct about appeasement or not (which he seemed to be), however, at that point of his career he was politically 'in the wilderness', so many people at the time thought he was being ridiculous.
Here's something I wrote in an essay about Churchill's view of appeasement:
"Churchill's opinions on the policy of appeasement prior to World War 2 are evident in his book, 'The Gathering Storm', in which he infers that he could have prevented WW2 had he been in power in the interwar period. Churchill claims that "there can hardly ever have been a war more easy to prevent than this second Armageddon". Churchill, whose career up to that point had been littered with catastrophic mistakes and misjudgements, had nonetheless led the minority that correctly understood the menace of Hitler and the dangers of disarmament and appeasement. Churchill's willingness to record the past allowed him to reinforce his judgement on appeasement, and hence he has been credited with recognising the failure of appeasement attempts and the danger that Hitler posed to Europe."
Some other historians argue that Churchill was only worried about Hitler and Nazi Germany because of the threat they posed to the balance of power in Europe (i.e. Churchill didn't want Britain to lose their dominance). The Darkest Hour film has some good quotes about appeasement too.
Hope this helps a bit!