Like another poster said above there's an extremely in depth tutorial in game that's absolutely great at explaining the core mechanics.
Okay, now that we've got that out of the way, you're 80% likely to forget those same mechanics the moment you finish the tutorial. There are just way too many characters (not in the street fighter sense--each character is ridiculously diverse) and you're going to have a headache remembering basic strings because they all play differently.
So we understand that it's hard, the tutorial only gives a rudimentary feel for the game but we're feeling confident. Probably enough to take on arcade!
No, I wouldn't do that. The first few matches fine, but once you get to the last it's just a shitty day in the neighborhood. So we've returned to point A.
Point A dictates that we go learn specific character moves. Who caught your eye in the tutorial? No one? That's fine, that's why you get a story mode! Go ahead and play it out! You'll find a character or two that works wonders for your style. Then go learn their combos! How? There's a mode for that too! How lucky right?
But you're dropping combos left and right with the analog stick...so my advice would be to switch to directional buttons mainly (unless its uncomfortable, but they're so much better for reaching specials/supers and chaining combos). Also, I'd try not to rely on Stylish too much and learn the classic gameplay.
Other than that, BlazBlue is an awesome game! Enjoy the ride.