I don’t think I’d start with Brothers Karamazov—but that just be me and how I approached Dostoyevsky. (But, you certainly can!
My suggestions:
Notes from Underground is an extremely rich novella. If you don’t have a background in 19th century idealism or fundamentals of philosophy, I’d encourage you to look up things that are unfamiliar to you while you read to get the most out of it.
The Idiot is an oft overlooked novel of his that I think is excellent. It’s a bit more approachable than Crime and Punishment and Brothers Karamazov (i.e., smaller character list, more direct storyline).
You really can’t go wrong with Dostoyevsky, though.
If Russian lit is an interest, give Bulgakov’s The Master and Margarita a shot.