Coil elements are more efficient and you don't have that hot glass warming the air afterwards. With energy rates only going up, efficiency will become more and more important. With any electric cooktop you need pans with good flat bases. No large part of a coil element should be glowing orange while the pan is on an element that is on high.
Whirlpool makes some nice coil top ranges. With plug out elements on the stove top, if you make a big mess while cooking, just put the pans and rings in the dishwasher and they will not be too hard to keep clean.
One word of warning about ovens with concealed bake elements: They are slower to preheat since the heat has to come through the porcelain and the intense heat under the bottom of the oven causes damage to the porcelain. Any fruit juice which is acidic like juice from a pie that drips on the very hot porcelain etches it. Even after you clean it, it will be a dull patch in the porcelain. Maybe you won't have the stove long enough for the bottom to rust through, but that is the final chapter in the story of putting the bake element under the porcelain oven bottom. It was tried in the late 40s and very early 50s by some manufacturers and that is what happened then. KitchenAid said that would not happen with porcelain that was designed for self-cleaning ovens, but they are wrong. First of all, you do not self-clean an oven every time you use it. Second, when you bake in an oven with the bake element in the cavity, the oven floor is not hotter than the rest of the oven like it is when the heat from a 3000 watt bake element has to go through the porcelain to heat up the oven. Third: heat that radiates down from a glowing bake element in an oven is partially absorbed by the oven which helps heat the air inside it and is partially reflected back into the oven. In spite of all the insulation that is put under the bake element when it is under the oven, the heat that radiates down is traveling away from the oven instead of into it. The heat does not all escape, but it is slower to be used in heating the oven and the design is therefore less efficient. Finally, when you have a bake element in the oven cavity, you can put a piece of foil on the floor of the oven UNDER THE ELEMENT to catch drips. You can't do that with the concealed bake element because the oven floor runs so hot that there is the possibility of fusing the foil to the porcelain.
Enjoy your new electric range.