Here's a good listing of all the cars. It shows whether a car is tradable or not. It also tells you if it is a prize car that you can win in the game from some of the races or licenses. You can even sort by manufacturer, level, drivetrain, or country if you want to narrow the list down to a certain make or feature.
One other neat feature about that site is you can create your own virtual garage and list all the cars you have to help with trading. You can also add notes to each car to include short details like color, if the vehicle is 0/0/0, or from the UCD. Here's an example what a person's garage looks like:
So if you want to trade with someone all you have to do is give the link to your garage (like I just did above) and tell that person to pick something from your garage.
Anyhow, welcome to GTPlanet. There are a few stickies at the top of the forum that you might want to read before you do something to anger some of our not-so-patient members of the forum.