If we take as a given that Lutherans will honor and obey the governing authorities in determining what constitutes a legal marriage, there is then the question of an appropriate context in which to sanctify and celebrate that holy matrimony with the Word of God and prayer. It is certainly holy in and of itself, as an institution of God, because it is sanctioned by His command and promise and governed by the authority that He has established in the world. As in all things, however, we pray that marriage would also be sanctified unto us Christians by the Word and Spirit of God, that the bride and groom would enter (and henceforth live within) this holy estate in faith and with thanksgiving. To serve that purpose, the Church orders herself and the service of God according to various rites and ceremonies, which in themselves are free, but which are agreed upon in love for the sake of common corporate prayer and thanksgiving.
Marriage itself is not a private affair, but one that concerns both the commonwealth of the world and the corporate life of the Church as the Body of Christ. Weddings, therefore, are not a family affair, nor the special prerogative of the bride and groom, but public gatherings of the Church in the Name of Christ Jesus for the sake of the Word and worship of the Holy Triune God. Special circumstances and considerations ought to be handled as matters of pastoral care and discretion, with a view toward the proclamation and confession of what the Lord has to say about marriage. As in the case of funerals and commemorations of the saints, there is surely a place for particular attention to the couple as the object of Christ's grace and mercy, and as a living icon of Christ and His Bride, the Church. They also give public witness to the Church's faith. All of this finds its place within the context of that which the Church has collectively agreed upon.
The service books of the Church include the rite of holy matrimony, whether in the pew edition of the hymnal or in the pastor's agenda. Ordinarily, this official rite will be respected and followed, taking into consideration its rubrics and its measure of flexibility for local situations. Pastors have a responsibility for implementing the rite, and perhaps there will be ways in which the rubrics are adjusted or set aside in Christian love.
One example of an exception to the official rubrics, previously mentioned, is the point at which the rite of holy matrimony is administered in relation to the prayer office or Divine Service. The LSB specifies that it should occur at the very beginning, that is, prior to the service. I assume this goes back to such precedents as Dr. Luther's "Order of Marriage," in which the actual rite of holy matrimony occurs outside the Church door (followed by a service inside). I prefer to administer the rite following the reading and proclamation of the Holy Scriptures, and thereby give the Word of God free course to lead the couple (and the congregation) to the divine work and blessed gift of holy matrimony. I have found this to work beautifully, not only from a theological and liturgical perspective, but also from a logistical and practical standpoint. There is a natural progression from the Word to the marriage rite to the Church's prayer, praise and thanksgiving.
Now, as to the particular order of service in which the marriage rite ought to occur, I do not believe there is any one right answer. The rubrics allow for either one of the prayer offices (Matins or Vespers, Morning or Evening Prayer) or the Divine Service of the Holy Communion, or for the marriage rite to stand apart as an order of service in itself, in which there would be incorporated the reading and preaching of the Holy Scriptures. Different circumstances will suggest which of these may be most appropriate, and that will largely be a matter of pastoral care and discretion (again), which should obviously take into account the cares and concerns of the bride and groom and their families. When I speak of pastoral prerogatives, I am thinking not of a heavy-handed approach, but of responsibility for the administration of the Lord's gifts.
I tend to agree with the wisdom I have heard from others, that many weddings, sadly enough, should probably not be sanctified and celebrated in the context of the Divine Service. It would potentially be very difficult to exercise responsible pastoral oversight with respect to admission to the Holy Communion; and where that could be managed with clarity and integrity, there is likely to be offense given to guests who are not communicants of the same confession and fellowship, who would not be admitted to the Lord's Table. Having said that, however, the Holy Communion is surely meet, right and salutary in connection with the rite of holy matrimony, as it is a foretaste of the Marriage Feast of the Lamb in His Kingdom. The union of Christ and His Bride in the giving and receiving of His true Body and Blood is the very great Mystery signified by the union of husband and wife in heart, mind, body and life. So also, this Holy Sacrament is a singular blessing to the bond of holy marriage, in which husband and wife are called to live together in faith and love, serving one another and forgiving one another as God in Christ so does for each and all of us. Accordingly, where responsible pastoral care and oversight can be exercised, and unnecessary offense avoided, a "nuptial mass" would surely be an appropriate option.
I suppose it needs to be said, for the sake of clarity, that the bride and groom should not be communed apart from the congregation. That is to say, all communicants in attendance (of the same confession and fellowship) should be welcome to receive the Body and Blood of Christ.
In particular, if a wedding is to occur on a Sunday morning or in connection with a Feast of the Church Year, I should think that the Divine Service would be the "default position," barring any extenuating circumstances that would prevent it. In the latter case, then better to shift the date of the wedding than to forego the Holy Communion on such a festive day. It's all about Jesus, including the wedding and the marriage; so whatever is done should be determined accordingly.
Where the Holy Communion would not be feasible or advisable, one or the other of the prayer offices provides a very appropriate context for the rite of holy matrimony. Aside from the obvious consideration of whether the service will be in the morning or the evening, which of the offices to use will largely depend on what the customary practice of the congregation is. Where there is no such standard in place, then I would offer the suggestion of Matins for the morning, Vespers for early or late afternoon, and Evening Prayer for after sundown. I guess that's pretty obvious.
As far as the location of the wedding is concerned, my preference would certainly be for the church. Not because it's prettier (though it generally is), but because it confesses the theological significance of marriage and most clearly points to Christ Jesus and His dear Bride, the Church. Nevertheless, it is not the building but the Word of God and the prayer of faith that sanctify the location and the occasion. If the wedding is not to be at the church, then whatever may be possible should be done to establish an appropriate decorum in the space that will be used. It may be in such situations, as well, that the marriage rite would be used on its own, rather than in the context of any other liturgical service. Surely it would not be the place for the Divine Service of the Holy Communion.
There is more yet to say, concerning such things as ceremonies, customs and traditions, the propers, and hymnody, but all of that will have to wait for another day.