EDIT - Sorry. Misread your first post and thought your stereo already has WiFi built in. Disregard what I wrote below.
The answer is not always easy since whatever you first try may not work, so purchase from a store with a strong return policy.
The best solutions in descending order are cat 5/6 cable, MoCA, Powerline Home Plug, WiFi. I don't know where Bluetooth falls along this path.
There a couple of ways of setting up WiFi as well: One AP or one AP plus one Bridge/Repeater. It all depends on distance from the AP, interference from objects in the signal pathway (walls, furniture, plumbing, electrical, glass, etc), interference from electrical devices in and around your home, and interference from neighbor's WiFi signal.
If all you want to wirelessly transmit are MP3's, then WiFi may be the least expensive and easiest solution. An inexpensive remanufactured router may provide all you need. One thing to keep in mind is knowing what your needs are. If you have no other use than streaming MP3 then try WiFi first.
You also might want to figure out what the NIC adapter is in your stereo before purchasing a wireless router. Is it wireless B, G, or N device? Does it have one, two, or three radios (and have 1, 2, or 3 antenna) - with maximum theoretical speeds up to 54 Mbps, 150 Mbps, 300 Mbps or 450 Mbps? Does it operate only on the 2.4 GHz band or is it a dual band device capable of operating on both 2.4 and 5 GHz bands? If the stereo device is B or G rated and incapable of speeds greater than 54 Mbps on the 2.4 GHz band, then your choice of a wireless router may be even lower cost as long as you have no other wireless needs and are not concerned with any new devices able to use wireless N in the near future. Lastly, make sure you are able to use the highest security level possible based on the NIC adapter device in your stereo, with WPA2 being the most desired.
Try to match up your needs with the specifications/limits of your hardware, including other needs besides your stereo now and in the near future. Purchase from a store with a liberal return policy where you do not pay a restocking fee or other penalty. You won't know what will work satisfactorily until you try.