Don't need an amp---the speakers are self-powered. That's part of the beauty of this system, the simplicity. If you go the passive speaker/integrated route you have used/thrift store options, but if you're in a little place you would be best off with a system that uses powered speakers anyway. I've got a CD playing* system made mostly out of used/thrift store gear. I'm using a Yamaha AVR, a pair of a/d/s 400e speakers [1980s/90s], Topping E30/L30 and a Sonance mini-sub. The CD player is a Sony Blu-Ray player I got for something like $6, the remote I got from Amazon was about $10. Total cost: around $450. It's got more bass and probably plays louder than those little self-powered speakers, but when you eventually find yourself living in someplace bigger [and get bigger speakers/amps] you will still have a really good source for CD playback, not to mention USB links for computer audio.
*But I mostly use it for computer audio.
We should perhaps mention that if kvlou choose passive speakers and amplifier Aiyima a07 then he needs to buy an external power supply in order to make it work. This considering it should be easy, plug and play and so on.
Kvlou, tips, with passive speakers. Select a amplifier that only need to be plugged into the wall socket with a power cable. CD player, speakers and amplifier are connected with speaker cables and rca cables. Connect, play music and be happy.
Do not invest big money in the cables. It does not matter to the sound.
Edit:
Then practical aspects, think about whether
remote control for amplifier and or CD player is something that is convenient to have.
There are
CD changers where you can put X number of CDs in. if it is preferable.
Do you have a small room. Do not miss to think again
if the speakers fit, purely physically, as you intended. If the speakers fits in with the other furniture in the room. Classic mistake not to think about it. I myself have missed it several times.
Speaker cables can be routed in cable canals. An easy and cheap way to "hide" the cables. See attached pictures.