Hello and welcome to the forums.
First things first, just start training. Don't over complicate it, just get out and run, grab a bike and start putting down the miles, and get in the pool and start practicing your form.
I think swimming is the simplest of sports, but the most difficult to master. So I would suggest getting a membership at a local YMCA, or community pool and get in the water. Your going to focus on the freestyle, go on youtube and search for triathlete and freestyle swimming. This will get you started on learning the basic techniques.
Bike does NOT need to be complicated or expensive. I rock a 88' Peugeot 12 speed I bought for a $150. Again don't over complicate it, just get on the saddle and start peddling. Again, youtube is your friend. As you go along you will learn more. You don't need fancy jerseys, clip in pedals, tri bars, aero helmets, none of that is going to make you win in training.
Running, you want a good pair of running shoes. Don't go by what the sales person tells you is the hottest shoe, go with what fits your feet. Unless you have specific orthodic needs, keep it minimal or a neutral. Most good running stores will have a treadmill and will have you run on it and make a short video of your 'gait', this will help determine the correct shoe for you. Again the concept is simple, get out and run, start putting down some miles. I really enjoyed a subscription to 'Runners World' when I first got started.
Once you start training and getting some miles down you will start learning more and more about what works and what doesn't.
First things first, get out the door and train. Just get started, don't think about it, just do it!
Cheers