All four are correct for your situation; they just have slightly different meanings. You can also use very with any of the four choices. Think about it: all four are adjectives, so if using one is grammatically correct, then the other three will be as well.
I would alter the sentence a little, but the way you've phrased it is not wrong.
I'd put it like this:
Wow, what a * question!
Or like this:
Wow, that's a * question!
Replace * with any of the four words; all are equally correct. The use of what or that's focus the exclamation a little bit more, making the sentence a little more versatile, but aren't strictly necessary.
How about the differences in meaning?
The standout of the four words you're asking about is long; the other three are quite close in meaning, but long is distinct from them. If you say what a long question, you're remarking on the length of the content. A long question uses a lot of words (or pictures, charts, etc.) to ask.
A question described as big, huge, or large might be long, or it might be weighty, substantial, or of great significance or importance. A big question might be long but unimportant, long and important, or important but short. Here's an example of a question which is big but not long: what is the meaning of life?
Big, large and huge are all extremely close in meaning, but have slightly different magnitudes. Big and large are roughly equal (I would rate big as slightly bigger, but this is largely a matter of opinion), and huge is significantly larger than either of the other two.
Since you want to describe the length of the content of the question, long is the unambiguous choice, but you can call it big, large or huge if you want. People will understand that you mean the question has a lot of content, though depending on that content they might think you also mean the question is important or substantial in meaning.
Your second example "I'm going to start finally" sounds odd, because "start" and "finally", near-opposites, are juxtaposed. (One almost always starts at the beginning, no matter how late one starts.)
I suggest
I'm finally going to start.
(this way, "finally" modifies "going")
or
"Finally, I'm going to start.
(this way, "finally" modifies the whole sentence; it's a sentence adverb.)
Best Answer
Of your examples,
is closest to meaning that you are learning to play the drums.
You could say:
because English is what you are studying.
But you are not literally studying the drums themselves (unless you want to make them), you are studying how to play them.
So it might be more natural to say: