Are there any specific supplications or acts to be recited or performed when purchasing a new home, and is there any basis in religion for reciting Surat Al-Baqarah or playing the Quran in the new home?

To fortify a new home, you should thank Allah for His blessings, hold a feast (Waqeerah), and remember Allah upon entering the home by saying: "Ma sha' Allah, la quwwata illa billah (What Allah wills, there is no power except with Allah)." And praise Allah when you see something that pleases you by saying: "Alhamdulillah alladhi bi ni'matihi tatimmu as-salihat (All praise is due to Allah, by Whose grace righteous deeds are perfected)." Also, recite the prescribed supplications upon entering the home, such as: "A'udhu bi kalimatillahit-tammati min sharri ma khalaq (I seek refuge in the perfect words of Allah from the evil of what He has created)," and recite Surat Al-Baqarah, which expels Satan from the home.