Very small Integrated and speakers used

Well, for $200, the little jawbone Jambox is unreal for its size. You just need an iPod - it can connect with a cord or Bluetooth. For a dorm room, it might be perfect.

Get a pair of used Quad 9Ls and run them directly off of your Iphone/Ipod/Ipad/laptop or better yet a used half-decent cd player. Surprisingly good sound for little money. I have them on my computer.

***Dealer disclaimer***

I set up a Roth MC-4 Music Cocoon for my wife. Its a small tube ipod dock. It also has inputs on the back, so you could add to it. It's 15 WPC. I've ran it with some small matching Roth speakers, some small PSB's too. At the moment, it's hooked to a mid size pair of Roth towers. It actually sounds pretty good. It's only 7.5 inches wide, by about 6 inches deep.

I also set one of her friends up with a Fatman Carbon II. Pretty similar. The Fatmam is 25 WPC, and a little bigger unit. She has hers on the kitchen counter.

I don't see many pop up used, but, I usually have some as B stock. Depending what you want, you can get something as cheap as $250. Might fit the bill.

My budget is around €300. I'll probably hunt some bargain on ebay.
I wouldn't minde tube/hybrid but it probably is not as reliable and safe and small.

Powered I was looking at: Yamaha HS50, Adam a3x or audioengine

As for amps theres a few:
NAD c326bee
Yamaha S500
Creek Evolution
Audiolab 8000 series
Rega brio 3, mira
Pro-Ject Stereo Box S (?)

What is out there from Chinese brands? I came across the Maverick Audio A1 but it seems more headphone oriented

As for passive speakers i don't know. Back home i have an old Kenwood KA-52 with Monitor Audio Silver S1 speakers. I was also wondering if i should bring them to my dorm but sometimes i go there.

btw i already have an external audio interface/dac

Audioengine 2 or 5. I use the 2 on my desktop. It's good for streaming services such as MOG. I had worse when I was a student.