New to swimming want to do a triathlon

I'm flirting with the idea of training for either a sprint or Olympic triathlon and am currently trying to get a base in each discipline. I had no delusions that swimming would be easy but after going to the pool today I feel blown away with its difficulty. My real question is how discouraged should I be from my initial performance today. Swimming 50m without stopping seemed to be just about my max. So I ended up just doing 25m at a time trying to focus on doing proper technique but even this felt very uncomfortable, short of breath etc. So for someone who has never taken swim or swam laps is this normal and how long would it take someone in my situation to develop the requisite amount of ability to start a tri training program? This is what alarmed me the most the triathlon training programs I have looked at I can definitely perform the first week of suggested training for running and cycling but swimming has 2x200m sets that I can't perform and certainly not comfortably. Even the 100-200m warm up seems too hard if it is without rest because as I said even when I tried to do lengths at a very slow focused pace I had trouble. The slow pace made me feel as though I was sinking I think. The book I am looking at has some base levels of ability before starting the program which for swimming is being able to swim for 20 minutes. I am assuming this means 20 minutes straight without rest which seems very difficult for me. So sorry for the long post but how long should it take me to improve to this level and what would be the best way to go about it? I have plenty of free time at the moment and can practice swimming as many days a week as is optimal. Any advice would be appreciated.