Because you are a beginner quilter and this is a gift so you want it to be extra nice I recommend doing walking foot quilting with your DSM. Without knowing the block size or the finished quilt size or even which setting you used for your LC blocks (there are many, barn raising, straight furrows, streak of lightening, pinwheel, just to name a few), I am assuming it is a mini piece based on your description. Even if it is a larger size like a throw or wall hanging, I feel one can never go wrong with the Baptist fan design. The Baptist Fan can be done with a walking foot or FMQ but as a beginner I would strongly recommend using the feed dogs and the walking foot. You will be much happier with the end result.
However, based on your thread description (A superior product in variegated colors) I am thinking you have King Tut which is a fairly heavy cotton thread. In my experience, variegated threads, especially heavier ones like King Tut don't look very nice when you have to backtrack or travel over already quilted lines. The build up shows a lot and the variegated colors can get muddy looking. There are ways to do a baptist fan without traveling (here is a link to a panto to give you an idea of how to do it:
https://www.quiltingstencils.com/Con...-5_p_1956.html ). You would need to mark so you probably want to make a template to mark it or find a stencil. Or you can pick a different thread, something not variegated and quilt the baptist fan with traveling.