All of these modes are just variations of the same set of options. So, for customization purposes, it does not matter which you select to use as a base.
VIP In standard VIP each team is assigned a VIP and players score points by killing the opposing team's VIP.
Rocket Race is a variation of Escort that has 2 man teams, invincibility and rockets with infinite ammo. The objective is to get your VIP to specific territories that look like the hills in King of the Hill. This is done by getting on a mongoose (the VIP cannot drive), with both of your players trying to knock other teams off course with your rockets, while trying to reach the territory first. The only way to kill anyone in this playlist is by a beat-down, though doing so will not benefit the killer except for the fact that the victim has to respawn.
In this game mode, only one team has a VIP. Teams take turns on offense and defense.
This game mode is similar to One Sided VIP in that only one team has a VIP. However, in Escort there is an added objective: the VIP can score points by arriving at checkpoints. A common strategy is to use vehicles to drive the VIP to the destination. Take note that the vehicle use settings for VIP's are set to passenger seat only, forcing the VIP's team to drive. This was made famous by Rocket Race, where there are four teams of two and the VIP must ride shotgun to get to the objective to score.
The key aspect of this mode is that special traits can be assigned to players who are in a specified proximity to their VIP (e.g. extra shields). The default setting is that both teams have such a VIP, though this can be changed.