I was wondering if it is a good idea to apply to a lot of programs that match my research interest and hope I get accepted by at least 2. Is that a bad idea or no?
It depends on what you mean by "a lot", but generally yes--As long as you can afford the fees and the quality of your applications don't suffer. I applied to 8 schools. I'd recommend anything between 6 and 15, depending on your research interests and any geographic restrictions. I would not recommend applying to fewer than 6 programs.