I think the answer as to why a website which describes "all types of pistol competition" doesn't really exist is found in the question: why would there be a website which covers all types of pistol competition?
You'll often find competition forums to be very sport specific, and very low traffic - usually. Although we all think it would be convenient to have a more centralized resource page, it's simply too much information for one site to really have, and too confusing then for readers. A web writer skilled in one discipline will typically not be skilled in most others, so their advice is not good for any but the one they actually know. And if anyone asks a question, they'll tend to get answers from all across the board...
Consider your own question - you asked about getting started in action pistol type competitions, specifically asking about IDPA. But then you got advice to start with Bullseye. That kind of off-the-wall advice is a disservice. But those folks who favor Bullseye will ALWAYS recommend new competitors to start with Bullseye. It reminds me of a King of the Hill episode when I was in school - one character was asking another for recipe advice on several recipes... The advisor would taste every dish and say, "add nutmeg...." Because she was strongly biased to favor nutmeg, in all cases. That's not good advice - nor is telling someone they should learn Bullseye to get into IDPA... But that's what happens when you ask a somewhat broad question in an even broader arena - you get broad, and relatively terrible advice.
The good news: it's 2017 and you are currently sitting at a computer - All of the rule books for respective competition types are all at your fingertips. Download all of the books for different types of action competitions, and read up on the rules. Search YouTube videos of the matches. Most association sites have local club listings or match schedules as well... It's all there. See which competitions suit your interest, see which fit your existing gear, or fit gear which you are interested in owning, and see which are available locally.
I will caution, however, be prepared to be disenfranchised. Shooting sports are exactly that - sports. If you're getting into Action pistol sports to supplant defensive training, you'll likey be grossly disappointed. Any of them will help improve your dynamic marksmanship, but all of them have specific rules, and specific rules will ALWAYS have specific "gaming" loopholes and work-arounds which will take away from their practical defensive applicability. Even when stage designers try to be creative and foster realistic scenarios, the concessions for safety or practicality usually over-restrict the dynamic nature, so it still tangibly loses something - OR it becomes so skill-specified such only shooters which have developed for that particular stage will have an advantage, and the rest of the fleet's scores are drastically offset (reminds me of ~20yrs ago the first time anyone saw a Texas star at a CAS match - a few guys used to shooting moving targets did well, the rest were blown away. But now, it's a common target, so everyone knows how to engage it). At the other end, matches with open ended designs which force the shooter to think on their feet usually end up fostering competition practices which don't apply in real defensive situations - I.e. Run up to this general area and engage this target array, which isn't shooting back, so no competitors will restrict their field of fire by utilizing the cover provided - they'll instead stand in the open to fire freely and quickly at all targets.
I know that's not the advice you were looking for, but I do encourage you to accept the fact you're going to have to do some searching to learn about these different competition types.
Better still - pick up your phone and push that picture that looks like a phone. Make some calls to national associations and local clubs. Get in touch - actual contact - with real people who can walk you through the high line for each competition type. You can learn more in an hour on the phone with a real shooter/club organizer/match director/national sanctioning advisor/etc than you can from a hundred hours of online reading.