I admire your determination to try this. Here's my 2 cents. First, you need to be able to dive reasonably well in order to get reasonably well-done photos. Essentially this amounts to the ability to hold a camera still underwater, in the face of currents and surges. You must have excellent buoyancy control. I think you need to start by learning to dive at least a little bit before adding a camera. You need to achieve some level of comfort before adding in more stuff to think about and more stuff to get in your way (or lose).
That said, I don't think you have to achieve excellent buoyancy before you start taking pics, only that you won't get many keepers until you do. Personally that meant about 10 dives for me. One thing about holding a camera underwater - it will motivate you to pay close attention to your buoyancy control, and as such can help you improve it. But you might also end up doing things like my wife, where she wasn't aware she was drifting down while photographing a lionfish and ended up ripping her eardrum. (She has a weak ear to start with, from repeated rips).
Cameras add to what can become an overwhelming amount of equipment for beginners, and they only make worse the effect of equipment problems. That's where you need to be comfortable diving before adding a camera. Drifting up? (Or down). Need to add or remove air 'right not' and don't quite remember what buttons to push and where they are? Not a good time to add a camera.
As far as the camera itself goes, the news is actually pretty good for you. As long as you can get by without external flash, you can do very well indeed with a camera outlay of less than $500 new. I'm talking about a (new) Canon Point-n-shoot with matching Canon dive housing. I'm on Canon #5 at this point (s120 is the latest), and they've all been decent to good with the newer ones always better than the previous ones. The housings are good. Get yourself camera, housing and an extra battery or two and you're good to go. Do NOT dive with a camera without attaching it to you somehow, or sooner or later it will drift away. For a point-n-shoot, get a wrist strap and put it on your right wrist soon after you enter the water. For a larger camera or one with external flash, have a lanyard that clips to your BCD.
Almost all the great dive pics I see are taken with external flash. However, having an external flash completely changes your diving experience as you can no longer just let go of the camera (dangle from wrist strap), or basically ignore it when not taking pics. You'll want to not use one until you are quite comfortable diving. They also have a tendency to get snagged in hoses and the like - not for beginners.
As for fearing underwater creatures, I can't really help you there. I have little fear there myself, so have no advice for overcoming it. Perhaps as others suggest a visit to aquariums might be useful. I have extremely rarely had any underwater creature attempt to touch me in any way. They are generally at least a bit shy (will swim away if you try to get close) or very shy (will avoid you as much as they can). You don't want to touch anything anyway, mostly because there is a lot of stuff underwater that can sting, certainly including fire coral.