The original question was about ideal speeds. Perhaps I wasn’t as explicit in my last post as I should have been. The ideal speed depends on the strategy your team decides to pursue. A robot design that attempts to have superlative perormance in all aspects, will rarely perform in any.
Is your strategy to get to the other side of the field ASAP? If so, ideal speed is as fast as your robot can muster. As Tom mentioned, just gearing for a high speed may not be enough to hit a high speed. The fastest may be a moderate speed robot that hits its highest speed by midfield.
If your strategy involves fine control, maneuverability, or pushing, then lower speeds will be of much more benefit. For most past games, torque and it’s matching acceleration has been much more important than speed.
Shifting gearboxes can provide for both speed and acceleration, with the trade of complexity and weight. Shifting is not a realistic option if your robot uses omnidirectional drive or mechanum wheels.
As an aside, the soccer robots I mentioned earlier used omnidirectional wheels, and could pull 1G acceleration in any direction. The same theory applies to omni and mechanum, as regular wheels or tank treads.
In short, we need to see the game, and your team will have to decide which strategy they will focus on. Ideal speed is strategy-specific and robot-specific.
Once the game is released, and your strategy is decided, then it is time to build and test a simple base with your chosen drive type. It doesn’t have to be your final design, just representative enough. Load it up to 120 lbs, and break out the stop watch. Run trials with each gear ratio you can, and see what gives your robot the optimal performance for your chosen strategy.
One last point; if your robot is going to be tall, with a high center of gravity, then make sure you approximate this on your test base. Too much acceleration with a high CG can be very bad. In this case, you may be better with a hi-speed gearing and lethargic acceleration.