This is all just my opinion and you'll no doubt get a lot of different answers about airbrushes.
I would expect to have problems with an airbrush that was bought for $40 with an included compressor. Can't imagine it's more than a single action air valve with no paint volume control.
That aside, most of the time when an airbrush clogs, assuming it's been properly cleaned, it's because the paint isn't thinned properly, or there are chunks in the paint.
Mediocre airbrushes are at least dual action which allows you to control how much paint is applied by moving the trigger back as you push it down. The type of airbrush also makes a big difference. In particular if the cup is attached to the bottom and sucks the paint up from below it's more for painting large surfaces, and needs higher air pressure so shoots more paint. Gravity feed brushes with the cup on the top are typically more for detail and more appropriate for model building type applications. It does take some practice to learn to use one for more than just painting something a solid color.
I don't want to start the whole Iwata argument, but the higher end airbrushes like the Iwata HPCS are a joy to use, and have good control for detail, Worth every penny IMO, but like most, I painted with Badgers for years before I finally broke down and got the Iwata.
For wood ship modeling I use a brush for most things. Airbrushes are great for plastic, and needed for a lot of good weathering techniques, but if you just want to paint a rail black a brush is just as easy and you can do it even after it's attached to the model.
Basically what I would say is if you don't get at least a descent airbrush like Paasche or Badger it's probably just a waste of money.
I won't say it can't be done but I couldn't have done this without an airbrush, but I used a regular brush as well. They are just different tools.