So glad you're willing to give this a try! Churches need organists, and especially Baptist churches, at least where I live. If you have adequate piano playing skills and a willing attitude you should be able to make some good music on the organ with a little practice. If your experience is like mine, the people will love you for it and will show their appreciation frequently. Your church's congregational singing will be tremendously improved with the right kind of organ leadership.
I was a Baptist all my life until I became a Christian (that's my little joke now that I've made the leap from the SBC to the Disciples of Christ denomination) and have a real heart for Baptist congregations and their singing. I played the organ for the same Baptist congregation for 17 years before changing denominations last year. I watched sadly as many of the Baptist churches in my area ditched the organ for a praise band, but my own church staunchly and proudly sang traditional hymns and gospel songs and used the organ and piano as primary instruments. I believe that more and more folks will tire of the rock and roll showtime churches and will eventually long for meaningful, stable worship that is found in the churches that stayed true to our musical traditions, and that's why I'm so happy to hear about your church and your willingness to learn the organ!
People vary greatly in their expectations of what the organ is to do in the service, or how much contribution it should make to the hymn-singing. My philosophy is that the organ should "lead" the hymns with power and authority tempered by grace and understanding! That is to say, the organ should be prominent enough to do its job of undergirding the hymns with clear sustained pitches, but not so loud or bright as to make people hold their ears. In a church where the piano shares the duties with the organ, the organist must be sensitive to the preferences of some folks to hear the piano as well as the organ, though the truth is that a piano is not by nature nearly as loud as an organ.
The organ need not be loud and bellowing in order to undergird the singing, but the sound does need to carry well. The 8'foundation stops of the Great manual, such as the Diapason or Principal 8 are normally the first to be included in any registration, but they are at the same pitch as the piano and the voices, so the organ sound will be muddy and lost if you use nothing but 8' stops for anything but the softest hymns. You should experiment with adding stops at 4' and 2' to complement the 8' sound, along with the mixture stop from time to time, especially on the final stanza of a majestic hymn. Reed stops, such as the trompete, may be brought in to give the organ tone a fiery sound when called for, but you don't want to use that type of tone all the time for hymns.
So, start with the Great manual and draw the Principal or Diapason 8, add the Octave 4 and possibly the Super Octave (or Fifteenth) 2. If you need more volume and body, you can also include whatever flute stops the Great has at 8' and 4' (possibly called Gedeckt, Bourdon, Hohlflote, Rohrflote, or Spitzflote on an Allen).
In the pedal division, use one or two of the 16' stops, depending on how much bass you want to hear. Add the Octave 8 and the flute stop at 8' whatever it may be called on that organ. You can also use the Great to Pedal coupler to give the pedals more presence.
With this simple registration drawn, play both hands together on the Great manual, playing the notes exactly as written in the hymnal. If possible, play the bass notes exactly as written on the pedals using both feet to smoothly move from one note to another. It isn't necessary to play the bass notes with your left hand, but if you're accustomed to doing that on the piano it doesn't hurt to play them.
There are a number of websites on which you can get basic information about technique. Check out these and others:
Playing the organ is different from playing the piano, to be sure, but do not fall for the old admonition to "never lift your fingers off the keys" or "play like the keys are covered with molasses!" Organ playing should indeed be rhythmic and often breaks between notes are essential. When playing a hymn in which the melody note is repeated, you normally need to lift your finger completely off that note for a fraction of a beat to separate the two occurrences. Otherwise it sounds like mud!
There are bound to be websites and youtube videos where you can hear good organ playing and good hymn technique. Perhaps some others will post their favorite examples. But nothing can be as helpful as simply trying different things in your own church until you discover what works. And never stop experimenting, never settle for the same old registration week and week, song after son. Variety is the spice of life.
The more you practice and play the more confident you'll become. Just be a good listener, let your heart and your ears guide you, and you will make a wonderful contribution to your church's worship.