Answer: You are lucky to have so much natural light, and you are also correct in considering the radiator as a possible problem. While it should be possible to have something blooming all of the time, it is a bit unrealistic for a beginner to expect everything to bloom all of the time right away. Many of the blooming houseplants are cyclical, meaning they bloom and then take a rest break and then bloom again.
With a little experimentation, you should be able to grow a wide variety of plants. Keep in mind that plants do not necessarily have to sit so close to the window, particularly since not all plants appreciate so much light. While the radiator will dry oput the air and create a draft, it is not an insurmountable problem. In my own home, I have grown a number of plants on a table placed up close to the window so that the table top overhangs the radiator but does not touch the glass. (This effectively deflects the rising heat around the plants -- but it may also play havoc with the room temperature and create unexpected drafts.)
Here are two primers of sorts on houseplants: http://coopext.cahe.wsu.edu/infopub/eb1354/eb1354.html and http://www.ianr.unl.edu/pubs/horticulture/g1022.htm which include some valuable information about general houseplant care, lighting and perhaps more important in your case, humidity. If you are serious about houseplants, you might consider purchasing a humidifier if the air in your apartment is dry.
In addition, here are care instructions for a number of commonly available blooming plants.http://muextension.missouri.edu/xplor/agguides/hort/g06511.htm
For a beginner, I think the holiday cactus, kalanchoe, amaryllis, jasmine and African violets would be the most likely candidates. Have fun with your plants!
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