Although I think it is a bit hard to pick one bowler as the greatest in the post-war period, one brilliant bowler who often gets overlooked is Alan Davidson. His record is impressive enough on its own, but when you consider he about breaks even in most categories when compared to the 70s and 80s bowlers like Marshall, Holding, Hadlee, Lillee, Khan and Botham, it is remarkable that be played in a period so dominated by batsmen and well known for flat batting wickets. The gap in class is evident both in stories about his bowling and in statistics.
Davidson played 44 tests between 1953 and 1963, and took 186 wickets at an amazing average of 20.53, with an economy rate of 1.98. Both his average and economy rate are much better than the competition from his time, and his average alone is the third best of any bowler after the war, behind only Tyson and the little known John Wardle, and maintained over a longer period.
A few other bowlers from the same period:
Hall - 48 tests, 192 wickets @ 26.39
Valentine - 36 tests, 139 wickets @ 30.32
Ramadhin - 43 tests, 158 wickets @ 28.98
Fazal Mahmood - 34 tests, 139 wickets @ 24.71
Benaud - 63 tests, 248 wickets @ 27.03
Lindwall - 61 tests, 228 wickets @ 23.03
McKenzie - 60 tests, 246 wickets @ 29.79
The only bowlers which really come close from a similar period in terms of average are Englishmen, and I believe English pitches were notoriously difficult to bat on during the period, and scores for both sides were much lower there.
Statham - 70 tests, 252 wickets @ 24.85
Laker - 46 tests, 193 wickets @ 21.25
Trueman - 67 tests, 307 wickets @ 21.58
Tyson - 17 tests, 76 wickets @ 18.57 (best post-war average by a fair margin, but only a very short career)
He might not be the best in the post war period, but he would have to break the top 5, and is regularly overlooked.
With regards to the original question, I'd find it difficult to seperate Davidson, Trueman, Marshall, Hadlee, Lillee, McGrath and Ambrose.
In recent years, McGrath is the best bowler I have ever seen on flat wickets, and Ambrose is the most devastating on wickets with something in them for quick bowlers.
