What will the source be? Hooked up to an amp & some kind of input? Or through your computer? Or straight from a phone/tablet via Bluetooth?
It’ll make quite a difference to the recommendations.
And what is ‘cheapish’? When I was looking for my first speakers, £100 was my max budget, but the other day I saw a kid about 10yrs old telling his mum that he ‘had to have’ a pair of Beats Audio headphones. They were £199. Things seem to have moved on since I was a youngster…
If hooking up to an amp, you could do a lot worse than a pair of these:
http://www.richersounds.com/product/standmount-speakers/monitor-audio/bronze-bx1-blk/moni-audio-bx1-blk
or their bigger BX2 brothers.
Regarding the mention of a sub, I would wait & see where you are staying. I had some fairly compact floorstanders at uni (still got them) and they were well overkill for the kind of rooms I ended up in.