Learning to love to run - tri beginners

Hello my name is Jackie and I'm very new to tri. My background: im generally active with different type of sports but never serious in one. Prior to start training for tri, I danced/ did yoga twice a week, run 1x, swim 1x (but not so good at it), play golf 1x. I was looking for a new challenge in life and was fascinated by tri as a sport and was inspired by many triathletes.
My goal is not to loose weight but rather to gain strength (petite 5'2" 105 lbs). I'm very new to this forum so open for any advices and tips from everyone. I hope to do my first half marathon by next April and first sprint by August 2016.
Nice to meet everyone!