First let me preface by saying that, no, I have not read Infinite Jest. I wanted to read his two novels in the order that they were written, hence Broom of the System came first. So I'm not going to spend time here comparing the merits of the two novels, since I can't.
Broom of the System is a strange, off-beat, inventive, hilarious and philosophical novel. DFW has a love for incorporating many view points and different styles of writing; in this novel alone we get transcripts, first person diary entries, stories within stories, third person and even a news release at one part. But that's not to say that the novel doesn't have a cohesive feel.
The plot is too complex to really go into totally, but it centres around the disappearance of Lenore Beadsman's grandmother, also named Lenore. Lenore, a philosophy major, has an overbearing and super jealous boyfriend, who also happens to be her boss at a publishing house in which she works as a switchboard director. She has a roommate named Candy Mandible, a wide ranging and bizarre family (of whom, her brother, LaVache with his drug habits and prosthetic leg, is the best), and a bird named Vlad the Impaler.
The style is kind of like a cross between Don DeLillo's dialogue and Kurt Vonnegut's social satire. But really there is nothing quite like reading David Foster Wallace. For those that are frightened of David Foster Wallace for whatever reason, don't be. His short story writing, especially in Oblivion, can be inaccessible and frustrating, but luckily Broom of the System doesn't fall into either of those categories.
This is the kind of novel that you can analyze, if you wish, and get into the philosophy, or you can just read it because it's hilarious. Win win, really.