Are qubits written in a big-endian or little-endian order when grouped? Say for instance you layout a quantum simulator like follows:

amps = [0] * 8  # 3 qubits

Therefore you are left with the following in binary: 
000, 001, 010, 011, 100, 101, 110, 111

Does the third digit in binary represent the third qubit or the first?

One would assume it would be the third but I'm not certain and I don't want to get the model wrong.
There's no convention. Usually the endian-ness doesn't matter, or else it's clear from the context which endian-ness is being used.

(I'm also not aware of a convention for whether the wires in circuit diagrams are top-endian or bottom-endian. I just always infer from context.)