They are both great exercises and you can get a great workout with either. The advantage that cycling has over swimming is that most people can do it longer which will burn more calories. There are people that enter 24 hour cycling events, few people could swim for that long.
As others have said, losing weight is more about diet than exercise. You want to exercise to strengthen your cardiovascular system which will improve your quality of life.
Since you are new to cycling, I wouldn't buy on line because you don't what you like. Go to a sporting good store or bike shop. If you have a Performance Bike near you that would be a good choice.
Last edited by Carbon Unit; 05-19-11 at 01:32 AM.