The answer to the question of what icons should be in the house should begin with a clarification that in Orthodoxy there are no rules that would determine how many and which icons should be in the house of the believing person. Usually, in the house of an Orthodox person there are icons of the Trinity, the Savior, the Virgin and the most revered saints.
One of the most famous and revered images of the Trinity is the icon painted by the icon painter Andrei Rublev. On the icon, the Trinity is depicted in the form of three angels sitting at the table and blessing the cup. This image is saturated with symbols and is a true theology in paint. The icon is revered by believers not only for the beautiful artistic performance, but also for the depth of the theological meaning that the author put into it.
Another icon with an important meaning for the believer is the icon of the Resurrection of Christ, in which Christ is portrayed as having overcome death and leading the Old Testament righteous out of hell.
Almost every family has a pair of wedding icons, which often become a family shrine and are passed on from generation to generation. In addition, these icons are usually given a central place in the home iconostasis. No less respected are the nominal icons, that is, the icons of saints, in honor of whom the believers received a name at baptism.
Above the front door of the house you can often see the icon of the Savior Not Made by Hands. This tradition is connected with the legend that tells the story of the ruler of the ancient city of Edessa - Avgar, who was healed from the image of the Savior and then ordered to decorate the icon richly and place it above the entrance gates to the city so that all those entering the city could bow to it.
Above the entrance to the house, too often hang the Ostrohbra or Seven-arrow icon of the Virgin. Often above the door you can see the icon of the guardian angel.
But nevertheless, it should be remembered that any icon is a relic with which one has to deal with the piety proper to it and not forget that its primary task is to encourage the believer to pray and perform good deeds.