Yeah, while the first Twisted Metal may be inferior compared to the sequels it spawned (especially Twisted Metal 2: World Tour and even Twisted Metal: Black). However, back in the day, this was well received.
The story for this is on Christmas Eve 2005, Calypso holds his infamous Twisted Metal competition in the city of Los Angeles. The single-player mode has you fighting through six stages as one of the twelve selectable vehicles, from series icon Sweet Tooth to low rider Thumper to the forgotten Pit Viper. The first level, Arena Duel, starts you off easy, as it's a one-on-one fight, but future levels, based around locations in Los Angeles, has more opponents, with Assault on Cyburbia having a whopping eight opponents. The goal of the single player mode is to beat all the levels, as well as the final boss, Minion, who is the winner of the Twisted Metal before this game's.
The graphics were one of the many complaints critics had alongside the length of single-player mode, but this was released back when the PlayStation launched, I can overlook it, as back then, 3D graphics and polygon models were not perfected (as seen in games like the original Virtual Fighter, which was released in arcades two years prior to this game). Each vehicle is a different type, and has different strengths and weaknesses (Mr. Grimm has a power special weapon and high speed and handling, but low armor, and Warthog has high armor, but low speed). The controls are pretty good, as the d-pad allows movement of your vehicle and the shoulder buttons are used to switch and fire weapons as well as fire machine guns. There are a lot of weapon pick-ups in the game, some only appearing here (like the oil slick and spikes) while others would be reworked into Advanced Attacks used in the sequel (mainly the Rear Missile, Freeze Missile, and Catapult).
Sadly, the story and endings are all text. There were ending movies, but they were axed due to an employee being offended by the violence and sexual content (although Jaffe would later said they would have hurt Twisted Metal). However, it is a good game, as the single player campaign is fun, and there is a two player mode for you to take on a friend.