The way you wrap up pretty much depends on what is comfortable for you. There are just two things that you must do: make sure the wraps go through each of your fingers and make sure there is sufficient wrapping around your knuckles and wrist. Chances are the boxing technique you found should involve these two.
As for gear is concerned, I am partial to Fairtex for Muay Thai. I have their shin pads, gloves, wraps, and shorts and they all have lasted a long time. Shin pads aren't needed for bag/pad work but they are definitely a shin saver when sparring. I use 14oz gloves for training and 16oz for sparring. I also got the satin Muay Thai shorts by fairtex because my trainer said they lasted longer, he said he has had his for 6 years and he still wears them. And as was said earlier, wraps don't really matter as long as they are elastic and comfortable.
We use fairtex thai pads at my place but i dont know enough about other company's pads to tell you which is better. But I do know that ours work very well.
Hope this helps!