You'll want to read Tsukihime before you read Melty Blood, seeing as Melty Blood is a sequel. It also uses some jokes from Kagetsu Tohya as well, but you can manage without reading that if you want.
As for the story itself, it's short and not very deep, but it has it's cool moments. A lot of the recurring cast is presented too deeply in their respective stereotypes so even with your knowledge of them they feel generic, but the new characters are designed and presented well. It wouldn't make a good novel, but it's the best storyline you'll find in a fighting game.