Microstates - Why Position and Momentum? Why is it that when we discuss the microstate of a system of particles, we use Position and Momentum? How does Position and Momentum tell us everything we need to know about a single particle? I've always been unsure as to why those 2 quantities are used instead of any other like Position, Mass, Velocity and etc.
 A: Position $q$ and momentum $p$ are the dynamical quantities relevant for classical motion. The Hamiltonian equations (here not in the most general form, but a useful form) are:
$$ \frac{d}{dt} q_i = \frac{1}{m_i} \ p_i$$
$$  \frac{d}{dt} p_i = F(q_1,...,q_N)$$
(where $i=1,...,N.$)
If you have given the initial positions and momenta of a system of $N$ particles, these equations give you as the solution the dynamics of the whole system, how position and momentum evolve for all times.
A: Luke's answer is great! For a different (yet the same if you think about it) perspective, just look at Newton's second law $$\vec F=m\vec a=m\ddot {\vec x}$$
This is a second order differential equation. To solve this we need (well dont need, but typically this is how it is done) to specify initial conditions $\vec x(0)=\vec x_0$ and $\dot {\vec x}(0)=\vec v_0$. Therefore, if we know the initial position and velocity of a particle along with the forces that act on it, then classically we know exactly where it will be and the velocity it will have at any point in time. Of course, $\vec p=m\vec v$, so anything we say about the velocity can also be said about the momentum (with just the difference of the mass of the particle). 
The focus on momentum rather than velocity, as has been pointed out by others in the comments and in Luke's answer, is because it is very useful in Hamiltonian mechanics. This is especially true when you make the jump to quantum mechanics. There we have a momentum operator, but you usually do not hear anything about actual velocities.
Also as pointed out by others, some systems are better defined using other quantities. For example, in looking at systems with rotational symmetry it is much more useful to look at angular momentum. It really depends on the system in question as well as what questions you are asking of this system. 
