For "with most of the support", if you mean the official Adobe one, it must be FlexBuilder(FlashBuilder) or Flash IDE. If you mean the community, I think all of them are very well supported.
And when you mean "coding", yes, Flash IDE is horrible. And actually you do not need it for debug since both FlexBuilder and FlashDevelop(with some tricks) are able to debug.
Finally there are at least two more IDEs, axdt and FDT, both are eclipse plug-ins.
