The most affordable 4" active speakers suitable for use as desktop multimedia monitors are currently the ADAM A3X. They will set you back ~ 400 Euro. Other manufacturers such as Genelec, Focal and Eve all make competing models but they are even more expensive.
If you have the extra space (~1" all round) you can get entry level 5" active monitors from the likes of Mackie, Yamaha and JBL for as little as ~250 Euro if you shop around.
At your suggested price point, whatever they say in the sales blurb, what you get is essentially a regular amp and speakers hi-fi system with the amp built into the cabinets. This means they are often better value vs a traditional separates system. The potential down side is that the manufacturer might have made too many compromises to meet a price point and you end up with reliability and self noise issues.
There is also a whole class of powered 'monitors' invented for the use of bedroom studio producers experimenting with basic DAW software such as Traktor, Reaper, Serato and Ableton. Brands to look out for are KRK, M-Audio, Berhinger, Fostex and Samson. I had a pair of M-Audio AV40 for a while. They are neither accurate nor very deep but they did have a typical audiophile sound. Especially nice with house or pop. They also broke down within a year.
So buy from a regular dealer you can trust to honour the returns and replacement policy in case you need to take advantage. Try and listen to a selection if you can. I don't have direct experience but in your situation I think I'd start with Samson or Fostex because they have the best reputation.