When you place a custom camera or path camera, you can select a keyframe (the little square on each end of the clip). Then on the left you'll have various options for that keyframe. Two of them are Target and Anchor. By default these are set to "-1-None". You can set Anchor to "Local Player" or to the name of the first ghost. This way the camera will stay in the same relative position to the car no matter where the car moves. Now you only need to move the camera close to the car.

Copy the data from the first keyframe to the last keyframe by first selecting the last keyframe. Then hold CTRL and click the first keyframe. It will copy the data from the keyframe you click... and paste it onto the keyframe currently selected. This way the camera doesn't move between the two keyframes but stays in the same relative position.

Target is useful for making sure the camera is always looking at the car. The only downside is that the car is always centered in the frame. Sometimes aesthetically this can get a little boring, so I try to only use it for just a few of the shots I make. I usually use Target without Anchor or vise-versa.

Another helpful clip is called "Editing Cut". This allows you to select a specific portion of the replay to render out to video, instead of rendering the whole thing and having to edit out parts you don't want later.