My church doesn't use it so I have only a passing knowledge of the book, and others who use it week in week out will have more to add. As you say, anything would be better than the unmentionable, and you won't go far wrong with A&M. That being said, I think Common Praise is better, unless you absolutely must have the newer items in A&M. It is also smaller, and therefore has the advantage of being easier to manage. I picked up a copy of the organ edition at a discount, and it is now my go-to whenever I play a tune from the Ancient and Modern stable (I sometimes prefer them to those in the Church of Scotland's Church Hymnary). It will certainly make your life easier, but is probably not essential if money is tight
The Church of Scotland is different, but I think most of these have come across as well.
All my hope: Most CoS churches seem to use Groeswen, though I play the original Meine Hoffnung. I would play Michael if I thought I could get away with it (and it is in the both the 3rd and the current 4th editions of the Church Hymnary, so some parishes must sing it)
Church Triumphant: I play the Youth Praise tune, which I quite like, and it seems to go down well with my congregation. CH4 only has Guiting Power, however
East Acklam - has it caught on? Not in Scotland in my experience. I introduced it to my church for last year's harvest but don't think it was known.
I'm still puzzled about Camberwell even though I grew up singing it. It is the only tune from Thirty 20th Century Hymn Tunes that has really caught on, and not necessarily the best of that collection either.
I have had Lord of the Dance at a wedding once, but never heard it anywhere else.
John Bell, of course, is very popular in the Church of Scotland. I don't know how well the Iona hymns are known in Anglican circles but a few seem to have caught on.