Will increasing or decreasing wheel size speed up an object? How does one change distance travelled through wheel size?
To increase the velocity of/distance travelled by an object with wheels, let's say for example a toy car *, which is more preferable: increasing or decreasing wheel size? The aim is to make the object travel at a greater speed (and therefore a greater distance) in a given time frame**.
Imagine the scenario on a frictionless surface (and no other factors that may affect the object other than gravity).

I know that increasing the wheel size will allow the object to cover a greater distance with each revolution of its wheels and therefore the object will travel further in the timeframe. I also know that smaller wheel size means a smaller circumference and more revolutions per minute (rpm), which will increase the acceleration of the object, allowing it to travel faster, which could also in turn increase the distance travelled in the given timeframe (?).

Which of these methods will increase the distance travelled in the timeframe, and if both will, which one will be more effective?

Notes:
*In other words, an object with wheels only; no motor, as the force applied will be from a human source
**I only have the resources to test one of these options so I am calculating the better option rather than testing both. I will conduct that experiment by allowing the object to travel until it stops naturally, then I will scale the distance to m/s.
 A: You should decrease the wheel size and try to make them lighter. Why?
When you input power into the vehicle, then you have a trade-off between whether to have more kinetic energy in the rotation of the wheels or in the translation of the vehicle. You obviously want the translation energy to be higher so you should choose wheels of less moment of inertia, i.e., less mass and less radius. 
$K.E. = \frac{1}{2}mv^2 + \frac{1}{2}I\omega^2$ 
This is precisely the reason why when a hoop($I=MR^2$), a solid sphere($I=\frac{2}{5}MR^2$) and a hollow sphere($I=\frac{2}{3}MR^2$) all of equal mass and radius are made to run down an incline the solid sphere reaches the bottom first and the hoop reaches last.
A: You don't state the time frame, but you could apply the kinematic equations of motions for both wheel sizes, assuming you know the ratio of acceleration between the two wheels.
I have assumed a level surface and a fixed gear ratio. 

I only have the resources to test one of these options so I am calculating the better option rather than testing both. I will conduct that experiment by allowing the object to travel until it stops naturally, then I will scale the distance to m/s.

It really all depends on how accurately you want to measure the effect of wheel diameter. But if you try various values of acceleration, it may be clear that here is an obvious advantage in one wheel size from  your calculations.
So if you obtain the acceleration figures, you can do it all on the equations, also F = ma will feature as well.

The above laws apply, and the angular version of them, is listed below.
${\displaystyle \omega _{\mathrm {f} }=\omega _{\mathrm {i} }+\alpha t\!}$
${\displaystyle \theta _{\mathrm {f} }-\theta _{\mathrm {i} }=\omega _{\mathrm {i} }t+{\tfrac {1}{2}}\alpha t^{2}}$
${\displaystyle \theta _{\mathrm {f} }-\theta _{\mathrm {i} }={\tfrac {1}{2}}(\omega _{\mathrm {f} }+\omega _{\mathrm {i} })t}$
${\displaystyle \omega _{\mathrm {f} }^{2}=\omega _{\mathrm {i} }^{2}+2\alpha (\theta _{\mathrm {f} }-\theta _{\mathrm {i} }).}$
I am sure there is a easy equation that links  wheel diameter to  acceleration, but it might be more complicated than that if weight  is an issue, as moments of inertia may then be involved. It depend on the scale/mass of the car 
Best of luck with it.
