Sounds like an interesting project you're working on Miriam. Let's get a better understanding of your situtation.
First, whether or not building codes apply to your location I would strongly recommend building according to code. This protects you from dangerous situations, helps ensure the structure's integrity long-term, and it increases the overall value of your home. For example, an open flame fireplace underneath a window is not code because the open flame could come in contact with window treatments. Obviously, you don't want this to happen.
How often will you use the sun room? If you are using it often or intend to keep it heated, then the heat needs to be regulated. Most fireplaces will not regulate heat well, or at all.
What type of heat does the rest of the house use?
How much space will you have under the window? It's not clear in the first post.
Is there any wall space, not under a window, where a fireplace could be installed?
Electric baseboard heaters are efficient electric heat and well suited to the narrow space below your windows. They also heat up an area relatively quickly and don't require much maintenance. You may also consider a wall heater that could use electric or gas.
Electric radiant floor heat would not be any more efficient and, as you already noted, more expensive to install. Radiant floor heat is subject to damage which is expensive to repair. It does not heat quickly and, because of the thermal mass of the floor, can overheat a room. So particularly if the room were used only occasionally radiant heat would not be the best option.
Well hope this helps, Doug