P1na: So it was random, as expected. Oh well, it's just a matter of getting to first place and then choosing. Thanks for the reply.
Well, not completely random. You have to waste the car you want to get if you want any hope of getting it. Here is the info taken from the Carmageddon Wikia page:
A Stealworthy vehicle is one that can be added to the player's collection before the end of the game. This gameplay mechanic features in the first Carmageddon game and the Splat Pack.
In those games, vehicles can't be bought for credits: they have to be unlocked. When the player wastes an opponent with a "stealworthy" vehicle while on the correct rank, there's a chance that their vehicle will fly upwards into the air, and the message "Car added to change car list" will flash on-screen. This means that the car has been added to the player's garage, and can be selected for use between races.
The Suppressor is the only vehicle 100% chance to be stolen upon its destruction, but the minimum rank requisite must still be met.
The player must waste the opponent themselves in order for it to count. This means they can't be pushed off instant-wastage cliffs or into mines. It should also be noted that it's possible to steal more than one car per race.
Also on the page are some rank requirements:
Rank Vehicle
89 Annihilator
89 Tashita Coupe
89 Grungebuster
55 The Twister
55 The Bear
38 Caddy Fat Cat
38 Towmeister
21 The Plow
9 The Suppressor
Of course, you can unlock all of the cars by completing the game or by cheating.