Recommendations are important during your application process. Therefore, firstly, ask whoever it is that you want to give you a recommendation if they will "give you a good recommendation." Why? I am an admission counselor myself and receive bad recommendations all the time.
As far as who you should get to write a recommendation for you, there are many factors to keep in mind:
1. We love seeing recommendations from individuals that have known you for a while. I love reading recommendations from teachers that can show how a student has grown, matured and become a better student throughout the years.
2. Always make sure that you get a recommendation from someone that has the time to write it for you. Teachers and counselors are very busy, especially during this time of year because they are writing so many recommendations. Make sure that you'll find someone that can spend some time on your recommendation and have a thoughtful response. Thoughtful recommendations are much better than a rushed recommendation, no matter who writes it.
3. If you are applying to a very specialized program, try to get a teacher that teaches in what you want to major in. These recommendations are sometimes important because it "proves" the type of college student you will be in that subject as well. However, getting a recommendation from that particular subject is not necessary. If you know a teacher or counselor that will write you an even better recommendation, get it from that person.
4. Try to get recommendations from individuals that know more of you than just your academics. Try to get someone that knows you academically, but can also talk about your activities on campus. These types of recommendations "prove" to us that you are a "well-rounded individual."
If the university asks for two recommendations, just send two. It won't make you look any better if you can get three recommendations. First, readers of applications might think that you don't know how to follow directions if you send in more than you were asked. Also, in my opinion, it seems as though the student is trying too hard by sending more than the required number of recommendations.
Good luck in applying to college!