>Crime and Punishment, Beyond Good and Evil
A lot of people will say not to start with anything too over your head right now, which isn't necessarily terrible advice, but on the other hand, it's important to challenge yourself, and often some of the books that spark a love of literature in many people are things they've read that were a bit over their heads (this was the case for me). Just because someone doesn't yet have anything interesting to say about the problem of evil or the existence of God doesn't mean the subject doesn't interest them and won't spur them to read further on the subject later on. You want to cast a bit of a wide net so you're able to find out what you like. Forcing someone to only read things they'll completely understand is probably as bad as overwhelming them with a ton of stuff beyond their comprehension.
If Dostoyevsky and Nietzsche seem like they would interest you and you really want to read them, I would recommend giving them a try, although you're definitely not going to have a good understanding of what they were trying to do right now.
Crime and Punishment is definitely the best place to start with Dostoevsky, and for Nietzsche, I'd recommend buying a compilation of his writing, like the Basic Writings of Nietzsche by Modern Library Classics.
>The Art of War
Unless you have a strong interest in military history, or you're planning to become like a cutthroat CEO or gangbanger or something, I'd put this off. Even then, The Prince might be a better starting point.
>Ten Little Niggers
I wouldn't consider this as a "big title". It's just a fun little mystery novel. It is really, really good. You should definitely read it, especially if you like the genre, but it isn't at all difficult.
Agatha Christie is actually a great author to start with early on. She's a highly entertaining and engaging writer, but she isn't at all difficult. Once you read one of her books, you're probably going to want to read another, and another, and so on. They're very addictive. More than anything, enjoyment is what will develop a love of literature, so while you definitely want to challenge yourself and step outside of your comfort zone, you also don't always treat everything like it's a homework assignment. Don't only read things because you think they're big, important books that will make you a better person. Also read stuff just because you want to read it.
Some more recommendations:
The Lord of the Rings
The Stranger
Short stories by HP Lovecraft (Bloodcurdling Tales of Horror and the Macabre by Del Ray is a good comp)
Short stories by Edgar Allan Poe (Complete Tales and Poems should be less than $1 used on Amazon/Abebooks plus shipping)
Mythology by Edith Hamilton
The Odyssey
The Republic (you might find it a bit boring, but read it anyway if you're interested in philosophy)
Essays and Aphorisms by Arthur Schopenhauer
Julius Caesar
The Killer Inside Me
The Collector