Suppose I have a projectile, fired at angle $\theta$, with velocity $v_0$, assuming it's only acted upon by gravity. How can I find an equation to enable me to plot the motion (vertical height against time) on a graph (I'll be doing this computationally)
You have to find the parametric equation of the trajectory.
With units in feet and seconds we get the following equations.
Note that your $$x(t)=(v_0 \cos \theta )t$$
and your $$y(t)= -16 t^2+(v_0 \sin \theta )t +x_0$$