I recently bought Deadly Premonitions from the bargain bin for the 360. I am loving it - few games before have demonstrated goofy surrealism such as what is found in DP. Though the graphics are slightly dated it doesn't really detract from the gameplay. What would be your budget game of choice?
Earth Defense Force 2017. Played over 80 hours of co-op mode and still going, it's the perfect chill out game. Friend comes over, we get food and drink, turn the music up and slay shitloads of alien bugs and giant robots. Most people just don't get it.