This is most certainly NOT Badger. Nowhere in the description the word "Badger" is mention. This is most certainly nameless chinese copycat, stolen design.
That doesn't immediately means it's crap. Some of nameless chinese production is pretty good, for its price. Most brandnames are produced in China, too, sometimes in the same factory by the same workers. Some of copycat production is undistinguishable from brandname. :) But in such cases you rely mostly on pure luck.
Single action external airbrush is comparatively simple piece of equipment; it will work, no doubt. Since it's that simple, may be it will work no worse than brandname, and in any case it would work not much worse.
Compressor is different. You see, compressors are relatively fragile things working in comparatively extreme conditions with at least one seriously moving part. :) I don't trust chinese nameless compressors - they would work for 3 month, for half a year - and then they'll die.
Mind you, I don't trust brandname compressors either. Genuine Badger may work for a year, year and a half and THEN die. Those small compressors just aren't made for a lot of work, they don't have stamina. :) Brandname compressors are definitely overpriced.
I would advise you to look for compressor in your local hardware store. I don't know how in your country, but here there are many small quiet cheap workinghorse "garage" and "garden" compressors, which are cheap even if a bit bulky, and will work for years and years and years.
And then you can buy a very cheap copycat chinese airbrush, for your first one. It will work. You wouldn't be able to draw "pencil lines" with it, but it will work. :)
Or buy the real deal, expensive brandname. Although in such case buy internal double action one.