I really want to improve my writing. I read books in the sci-fi and suspense/thriller which I love but, should I be reading works by the classical authors? If you have any thoughts about which books I should read, please share them. Thanks.
That's an unanswerable question really. It's only by reading several different authors that you'll start to learn. No one style is 'correct', but the more you read, the sooner you will start to notice what style you're naturally drawn to. After this you'll find yourself trying to emulate this style in your own writing, and then the next big step is finding your own voice and style. I've read a lot and I'm still in the 'emulating' phase. My voice is coming, slowly, but only because I write as well as read. I'm drawn to novels that use very simple prose and are not tightly plotted (if they have a plot at all). And it doesn't have to be only books in your chosen genre that you read. Good writing is good writing, whatever the genre.
And don't skimp on reading non-fiction (books on storytelling, especially.) Perhaps it was only me who had trouble 'seeing' what authors were doing without someone explaining it to me, but I found it invaluable. It doesn't really matter which ones you read first because, like novels, there are tons of approaches explained in these books and you'll find yourself picking up bits and pieces from a number of them as you put together your process. (my sig has a couple of recommendations).