hi shujaath, first of all, welcome to gmatclub.
Starting your b-school search can be quite a daunting task. As you start to do your research, you're going to form opinions about certain schools. These are your own knowledge and your own preferences working for and against certain schools. From what you have typed, I can tell that you haven't done much research just yet. My suggestion is to start browsing this forum more often and absorb as much as you can. You can also do a google search on business schools and look at some rankings, such as USNews and Business Week (BW). Harvard, of course, is one of the most elite schools, but as you research more, you'll find that Stanford and Wharton (UPenn) are also part of that league. Then you'll realize that UCLA Anderson and Duke Fuqua are also great schools. Anyway, these are things that you should do for yourself because you'll learn so much more from researching than from someone telling you what the good schools are. Once you form a list of schools, you can then ask the admission consultants if these are feasible, given both your undergrad and grad GPA (I can't be sure whether your 3.4 is undergrad or grad, but you'll need to present both numbers).
Here's a starting tip for you: there's really no "minimum score" on the GMAT to get in a "good" business schools. These are all very ambiguous terms that no one can help determine for you. What's considered "good" may not be as "good" for someone else. The moral of the story is to try to get as high of a GMAT score as possible. Remember - a high GMAT score doesn't guarantee you admission, but a low GMAT score will keep you out. Normally, 700+ is the score you want to set your target for if you're gearing toward any top business schools in the States. If you're far away from the published mid-80% range of a school's GMAT score, then you know that your GMAT score may not be as competitive.
Anyway, there's a lot of information circulating on this forum and on the web; start looking at some of them and think about what you want to do post-MBA, because that's also going to factor in what schools you should look at.
Good luck!