Yes, that is the most important thing for a beginner; to find the right music instructor. I did it for many years and am formally trained. Though I think that learning online is a great way to get a broader exposure, I don't think it's very good for beginners because it's a bit harder to communicate the basic mechanics. Also you and your instructor want to try to keep a balance between learning the basics and maintaining your level of enthusiasm/ interest.
Based on your level of seriousness, I recommend that you first write down some specific details about what you are trying to accomplish; like what do you see/hear yourself doing a year from now, styles, specific songs, ideas.
With that information in hand, start to search for an appropriate instructor by asking people at music stores, colleges and universities, friends and ads on craigslist. Interview the people and ask them if they perform professionally, if that is appropriate for the style of learning that you want.
Ask about their formal musical/teaching/performing experience. Also ask them how they would go about teaching you, and if you could talk to some of their students, and/or see their students play.
Then, if you find them to be a good candidate, definitely go to see them play live, to see if that is the type of style that you would like for yourself to learn in the future because that will be very informative.
Avoid instructors who don't have specific plans and shoot from the hip, improvise lessons on the fly.
Most important, have patience and take your time finding the right teacher. Try not to let the money limit your education.
For example, I am studying at the moment with a local singing instructor. He has 30+ years of professional performance experience and has formal training. He also studied with Bobby McFarrin. He understands all the mechanics and bio movements for singing properly. He has specific lesson and gives you mp3 audio exercises to do, and he makes custom mp3 lessons for custom problem issues. I have enjoyed watching his live performances at local clubs. In fact I'm going to see him perform next weekend with his band and an added four piece horn section. He implores all of his students to participate in live performances, in front of a live student audience, once per month every single month of every year on a stage with lights and a live band that he hires to back up each performer. He also records your performance on video and gives you a copy. All for a cost of $50/weekly lesson. That's the kind of instructor to ultimately find without going formal.
Best of luck in your search.