Buying an airbrush and compressor kit as one purchase is the usual route into airbrushing, and it is a reasonable one: the two halves have to work together, the hose fittings have to match, and a bundle removes a compatibility question that is genuinely annoying to research. The trade is that bundles are assembled to a price, and the compressor is normally where that price is found.
What a bundle gets right
Matched fittings are the obvious benefit. Airbrush hoses come in more than one thread standard, and discovering an adapter is needed after delivery is a poor start. A bundle also guarantees the compressor can reach the pressures the airbrush expects, which sounds trivial and is occasionally not. For a first setup, having a working combination out of one box removes several decisions at once, and those decisions are hard to make well before you have used the tool and know what you want from it.
Where bundles cut corners
Almost always the air side. A bundled compressor is more likely to be tankless, more likely to lack a moisture trap, and more likely to have a regulator that is imprecise near the low pressures miniature work uses. None of that makes it unusable, and plenty of painters work happily on a bundled compressor for years. But when someone upgrades a bundled setup, it is the compressor they replace, and knowing that in advance is worth more than the small saving the bundle represents.
When buying separately is better
If you already know you will paint regularly, buying the compressor on its own terms is the better decision: a tank, a proper regulator and a moisture trap are the three features that make airbrushing pleasant rather than fiddly, and they are rarely all present in a bundle. Buying separately also lets you match a modest airbrush to a good compressor, which is the right way round for the money. Someone unsure whether the hobby will stick is better served by a bundle, and there is no shame in that being the honest answer.
Questions people ask about airbrush and compressor kit
Should I buy an airbrush and compressor together?
A bundle is a sensible first purchase: matched fittings, a working combination and fewer decisions. Buying separately is better if you already know you will use it regularly.
What do bundles usually skimp on?
The compressor. Bundled units are more often tankless, without a moisture trap, and with a regulator that is imprecise at the low pressures miniature work needs.
Will any compressor work with any airbrush?
Usually, but hose thread standards differ and an adapter is sometimes needed. A bundle removes that question, which is one of its real advantages.