Which Airbrush/Compressor for miniature painting?

You definitely want an airbrush holder ($15-20) and a fine nylon cleaning brush set ($5-10). These are US prices and it will be higher in UK.

Most airbrush compressor should come with a regulator and moisture trap unit. If not, get one.

Thank you for the information and I think those are exactly the ones I am going to buy now. I just need help with one thing now - what else do I need for those items, besides airbrush and the compressor and somekind of a hose?

Sorry for the beginner like questions that most likely have been answered on these forums before.

The Iwata Eclipse HP-BS (0.35mm) & the Revolution BR (0.3mm) would both be suited to what you're looking for. Since you're in Europe the Harder & Steenbeck Evolution or Evolution Silverline would both be worth consideration - they both come with 0.2mm needle / nozzle combination "out of the box" which is ideal for the type of work you plan to do & have optional 0.15, 0.4 & 0.6mm nozzle sets available.

With regards compressors, your budget should allow a Sparmax model with a receiver - H&S market the Euro-Tec brand in Europe, these are re-branded Sparmax units, the 16A being their entry receiver (air tank) model.

A bit of shopping around should get you both a good airbrush & compressor for your budget - if you end up going for an Iwata airbrush, most definitely shop around as Iwata have recently had a price increase across the range. The Revolution BR & CR have suffered worst as the pricing on them has been held steady for several years, but with the Neo entering the fray as a new entry level airbrush Revolution pricing has increased. You should be able to find some dealers with pre-increase stock (& pre-increase pricing)still in hand.