This question is really difficult for me to discuss because I have never read Huck Finn before and also had no knowledge even of the basic story line. Literally the only things I knew about the book were that there is a boy named Huck Finn who is friends with another boy named Tom Sawyer, and that there is another book written about Tom Sawyer... So as for how my perception of the book has changed, it's more like I'm building my perception of the book, not changing it.
And so for me the first thing that made an impression on me is, rather obviously, the style of writing. I find it interesting how Twain writes out the dialect. It makes the book feel as though Huck is really talking to me, telling me about his experiences and filtering them through his own perspective in his own dialect. It gives me that intimate sense of being in his head the whole time without having to go through a proper narrator first. And that intimacy helped me understand Huck as a character much quicker and much easier, with all his personality quirks. For example, his beliefs (or lack of belief) about heaven were kind of childishly adorable, like how he "didn't think much of" going "around all day long with a harp and sing[ing], forever and ever." He rather hilariously has his own logic and writes off things that the grownups say that he believes sound stupid. I just love his character. The fact that Twain adds little details like this that help form Huck's perspective of the world helps me understand the choices he makes and views he has later on in the story.