Hi noexpguy,
to All Things Plants!
To my old eyes, the lovely plant in your photo appears to be a
Cane Begonia (Begonia coccinea) Begonia's require bright, indirect light (no direct sun which will scorch the leaves) and a well draining potting medium. Keep the soil moist but not soaking wet to avoid root rot.
I've never had much luck with cuttings transitioning from water to soil but many folks do it all the time. Hopefully others who are begonia growers will pop in with some helpful advice.
