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First of all, whatever you choose, make sure it's double action and gravity fed.

A couple of months ago I bought my first airbrush kit.

After A LOT of research, I decided to go for an Iwata Neo CN airbrush. It's great quality and reliable, as all Iwata products are, but still more economic, which makes it great for beginners. It comes with two interchangeable cups in two sizes, which I find very practical.
With proper cleaning and maintenance, it should last a long, long time. So far, mine has been a delight to use.
It's around 55 USD on Amazon.

In my case, I preferred buying from a known, quality brand. I'm not saying the more inexpensive chinese airbrushes can't get the job done, but I'm very meticulous with my works and I'd rather minimize the chance of an unexpected failure.

Paasche is another well-known airbrush brand. I found this kit which might also fit your criteria.

One strong suggestion: do not go cheap on the compressor. It's the motor that will power whichever airbrush/es you decide to get, so it's important that it's good. I'm not telling you to buy the most expensive ones, of course, but to avoid the cheaper, smaller ones.

I recommend a compressor with a tank. The tank helps store air at the desired pressure, avoiding pulsations in the air flow. This also allows the piston to only start when the pressure drops below a certain point, saving energy and piston life, while avoiding overheating and constant noise. Additionally, the tank helps condense the humidity of the air in it (it sinks to the bottom and can be emptied), thus decreasing the risk of water droplets suddenly coming out of the airbrush (getting an additional water/humidity trap also helps).

Here is an example of one such compressor (it looks bigger than it is haha).
There might be cheaper ones; just make sure to check the reviews thoroughly to check for possible common issues, and to make sure the company provides customer support.

No matter what you buy, maintenance is key. Learn how to clean your airbrush. Make sure you're using the correct cleaning product (for instance, it's not recommended to clean certain varnishes with alcohol, as they get sticky and it makes it harder to remove from the airbrush). Clean it as soon as possible; some materials dry way faster than others, so look into that. If you're not going to use the airbrush for a long time, applying some airbrush lube on the needle is a good idea.
Cleaning it is fast and easy once you get used to it.

Sorry for the long comment, and I hope it helped in any way! :)

There's lots of articles and videos online, too; just Google things like "Good airbrush for beginners" and "How to choose an airbrush".

*Edited because typos, and a formatting fail 🤦🏻‍♀️

Ah, thanks again! Here's the apoxie I bought: https://www.amazon.com/gp/aw/d/B0013UDWXI?psc=1&ref=yo_pop_mb_pd_title

Oooh sorry I misunderstood. You’ll probably need some sort of stand. I’ve propped my phone against tissue boxes or books to record short Instagram videos. They make phone stands for recording fairly cheap like this one that even has a ring light.