I inherited a kit, the cheap kind from Amazon, that had a crappy airbrush, air compressor, and some other stuff. I learned on that, but the airbrushes were not good, and it made learning even harder. I went ahead and recently bought a brand new airbrush pen, the "Harder & Steenbeck Infinity CR 2" which came with two different needle sizes and adaptors (not all airbrushes can use different needle sizes, so this saves money, imo). I almost immediately got to the fun part of air brushing with it and it's very enjoyable to use. It's on the high end, though ... and that's expensive ($320). Not sure what your budget is.

https://spraygunner.com/black-friday/harder-steenbeck-infinity-cr-2-in-1-0-15-0-4mm-v2-0/

There are a few ways you can go with this, though.

You can go with a super cheap kit (this is essentially what I started with):

https://www.amazon.com/Master-Airbrush-Professional-Airbrushing-System/dp/B009YNG21U/

A midrange airbrush kit:

https://www.amazon.com/Paasche-Airbrush-Double-Gravity-Compressor/dp/B08VF1SR26/

A more high end kit:

https://www.amazon.com/Steenbeck-Infinity-Miniatures-Compressor-Spraygunner/dp/B0BCH4D8CS/

There are also some relatively new air compressors that are handheld and rechargeable, but can get the job done and are a cheap alternative to an introduction to airbrushing:

https://www.amazon.com/Airbrush-KIBEE-Rechargeable-Handheld-Compressor/dp/B081HBK5K3/