Very small Integrated and speakers used

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.

you can get an emotiva xda dac-with volume control for $199 + (per yyz) some powered audioengine 2s for around $200 or less--should be a nice set up within your budget.