Eggs from the store need to be from a package that specifically says the eggs are fertile. Most store eggs come from all hen flocks and caged birds that have no roosters present to fertilize the hens.
As for the setup, it isn't a good idea. The ambient temp around the egg needs to be 99.5F so you need a guaranteed accurate thermometer.
A heat lamp isn't the way to incubate. It heats what it is aimed at and will easily overheat the egg contents. Internal temperature above 104 will kill the embryo.
You also have to be able to control humidity. About 40% for the first 18 days and about 60-70% near and during hatch.
Chickens need friends so you have to incubate lots of eggs so you have at least 2 successfully hatch.
If a nearby grocer like Trader Joes, Whole Foods or a farmer's market carries fertile eggs, then go for it. Check the Julian date on the carton which is the date (day of the year) that the eggs were packaged. If they're over a week old, don't bother.
You need an enclosure that introduces the right amount of oxygen and maintains a steady temperature and humidity.
Check the section that has information on building your own incubator. A small cooler can work.