I have something similar to what you linked to, the cheap airbrushes actually seem to work pretty well, but I haven’t tried a large high gloss surface like a model car yet.
I do have a decent badger as well and it seems worth the extra cost.
I have something similar to that from Aldi, the compressor is exactly the same, but I only got 1 airbrush and it was only a little bit cheaper than that one, so it looks good value.
I’ve only pissed about with it on bits of card so far, to try it out, but it seems to work great. I would say that it’s probably worth going for. You can always upgrade the brushes later on and the compressor only seems to run out of puff if you try to cover big (in relative terms) areas at high pressure, which you won’t be doing on a model.
I used Tamiya paint and it seemed to spray well, and you can either use airbrush cleaner or IPA to clean it (the cleaner spells exactly like IPA, so I assume that’s what it is).
I think I have a decent amount of patience until I watch something like that. I loved the way he let it evolve as he added the snow etc but didn’t over do it.