Assuming you have the starting position p_0 = (x,y,z) from ROS message called Pose and it's field Position and a list of coordinates = [(x_1, y_1, z_1), (x_2, y_2, z_2), ..., (x_n, y_n, z_n)], you can get the closest point by calculating a list of the lengths, e.g.

lengths = [vector3_length(p_0 - p) for p in coordinates],

where you have your function for vector3_length (2nd root of the sum of squared differences x_0-x_i, y_0-y_i and z_0-z_i)), then taking the minimum value with its index (enumerate etc.) - use it to choose the correct closest point.

If you want to get a more ROS-based answer, you should give us more material - as mentioned by @Ravi Joshi in the comments, ROS Tutorials is an excellent place to start.