The main reason to avoid using the matrix class is that a) it's inherently 2-dimensional, and b) there's additional overhead compared to a "normal" numpy array. If all you're doing is linear algebra, then by all means, feel free to use the matrix class... Personally I find it more trouble than it's worth, though.
For arrays (prior to Python 3.5), use dot instead of matrixmultiply.
E.g.
import numpy as np
x = np.arange(9).reshape((3,3))
y = np.arange(3)
print np.dot(x,y)
Or in newer versions of numpy, simply use x.dot(y)
Personally, I find it much more readable than the * operator implying matrix multiplication...
For arrays in Python 3.5, use x @ y.