For the OP, to make a celebration more liturgical in appearance and form, first and foremost, you must have a clear distinction between it and other forms of prayer, and of course, worldly distractions. It would be a good idea to use vestments rather than just civvies, although a choir robe with a stole (I think Presbyterians use them) should suffice.
Your music should not be of the contemporary “praise and worship” style, but rather the old hymns many Protestant composers have come up with (and many of which have been happily adopted by the Catholic Church, and I’m not talking OCP stuff).
Then base it on the basic forms that have come through the ages. One of the oldest descriptions is St. Justin Martyr’s. It clearly shows a celebration of the Word, and then the celebration of the Eucharist and Communion. Study the present form of the Roman Mass, since it has a simplified structure that can be easier to adopt. Also look at the Liturgy of St. John Chrysostom in use among the Eastern Christians. It’s a bit more elaborate but you may be able to pick a few elements, like the antiphons. Basically, a structure will require an opening greeting, a confession/penitential rite, a Collect (i.e. opening prayer), readings, psalms with antiphons, a Gospel reading, sermon, preface (the “Lift up your hearts/ we lift them up to the Lord” is common to practically all liturgical traditions), a consecratory prayer, the Lord’s Prayer, Communion, and dismissal.
Then of course, there is no liturgy without a calendar. Based on that, you can come up with collects one for each Sunday, and recite the Glory to God in the Highest after the penitential/confession portion. For starters, you can try following the Roman Calendar’s seasonal propers, and leave the sanctoral propers for later (these deal with celebrations of saints, which may or may not fit in with your theology).
I’d say you have your work cut out for you.
However, I’d echo a previous poster’s warning. You might fall in love with it and find yourself drawn to the Catholic Church.