Reading simple mesh data


Im now making a zombie game and got the terrain player and zombie somewhat up running.

Now my zombie is running a simple following script.

So he walks into walls if Im on the otherside of the house. I would like him to read a mesh that contains verticies connected to eachother, and choose one vert that is closest to me and get to it by following the connected vertecies in correct order.

I would also be able to see if the character is within a certain cubic area, if so then the vert on the cube is closer than any other vert.

So my question is:

If I have a mesh with verts and possibly also faces. How do I read their position and connections?