It seems to me that the single most important but neglected group that should be targeted for Christian evangelism in The West is adult men.
Men, because without a substantial and indeed organizationally-dominant male presence, any church will wither and die. Adult men - young and middle-aged, and the economically-active in particular - because this group has proved largely immune to mass evangelism so far.
(Christian evangelism can still be successful during adolescence and college years - although the ever-increasing anti-Christian competition from the mass media has severely diminished both the scale and depth of Christian conversion in this group.)
In principle, adult men may be a receptive group for the Christian message in the sense that they are perhaps the most deeply disaffected group in The West: their lives being divided between tedium (at work) and triviality (during leisure) - and both their status and self-respect being at an all time low. Indeed, adult, economically-active men are (on the whole) the major hate-group in the modern West: and there is a perpetual Open Season with regarding to blaming and attacking them for any and all sufferings and injustices (real or imagined).
So why has attempted evangelism in this group been so far ineffectual? Probably because of the weakness and smallness of real Christian churches - so that the chances are that there will not be any nearby, ready-made, vigorous, thriving, growing Christian church environment into-which a specific adult men can convert.
(The best or most real Christian churches are almost all small and precarious minority groups, in most parts of the West.)
Furthermore, the average Western man is easily distractible - and with a vast number of strong potential distractions upon which he depend on a daily basis to keep going - either real or fantasy escapes into status, power, sex, intoxication, vicarious excitement and the like. These behaviours are very difficult to repent and give up when someone's faith is still feeble, and they are staving off despair and demotivation precariously, hour by hour...
To convert from being a typical motiveless, nihilistic, shallow modern man to a strong denominational type of Christianity is a vast leap - almost beyond contemplation.
My suggestion is that there must be an intermediate step whereby such men can be converted to being 'stand alone' (non-denominational and unattached) Christians by means of adopting a new set of basic assumptions that immediately make them feel better: with a purpose and a meaning for life, and a plausible aim of becoming connected to the world - to God and other people - by real but invisible ties.
Such men need to be induced to challenge and discard the standard assumptions of modernity :- that life is going nowhere in particular and is therefore meaningless, that life ends in death and all good things are washed-away utterly, that there is no such thing as the soul but only bodies and brains, that the universe is indifferent to us, that we are fundamentally on our own in an uncaring reality and all the other unexamined notions that form the 'bottom line' for most modern people.
How might such men be reached? I think only as individuals - not as masses. So by the more individual forms of media but not the 'mass' media; and as individual human beings.
I think this may take a change in attitude from Christians who aim to do this - they must not push too hard or too fast, nor be too narrowly prescriptive in terms of doctrine etc. I think Christian evangelists should try to induce and support any changes in a positive direction; as being potentially likely to lead to further changes.
Indeed, I think the initial approach may need to be mostly non-denominational in the sense that the person being evangelized must never get the impression that they are being 'recruited' for a particular church - but rather 'saved' as a person.
The evangelist may need to internalize the attitude that where a particular convert happen to 'end up' as a Christian matters much less than that he be helped to escape from his current prison of brittle pride encasing despair and (often) self-hatred.