I'm rewiring an old chandelier. Any suggestions as to where to start?

Disassemble by starting with removing the sockets, and any center hub or junction points.

You may need to cut the sets of wires going to each socket at the junction hub, to allow the wires to be twisted while twisting the sockets off.

Try to find similar insulated wire, or you can use #16-2 SPT-2 , a 2 wire flat cable available in various colors.

Note that any two wire cable will have one wire "Identified" by ribs or markings in the insulation on one wire, use this wire for the neutral that connects to the threaded shell of each socket, leaving the other wire as the hot, connecting to the center contact on each socket.

Yes look around someplace like Lowe's or HD for wire similar to the old or wire you like, and look for the UL label and SP2. I can't say some of the stuff sold for speaker wire is approved. If the chandelier has the wires running in long tubes or something, you may want to use the old wires to pull the new in.