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/

I bought a slightly more expensive one ( here because I’m also using it for minis, but I’ve seen people use something similar to this and if it’s just for dice I feel like that should work just fine!

comment got removed for link so sorry if this shows up twice I would recommend this kit: https://www.amazon.com/Master-Airbrush-Professional-Airbrushing-System/dp/B009YNG21U. It was also my first starting kit. Comes with the compressor, some doohickeys that I still don’t know what they do, and three different types of airbrushes. The airbrushes are super super cheap, but it’s a really good place to start without screwing up an expensive one. I’ve also found that cheap airbrushes generally have looser tolerances compared to expensive ones. I’ve gotta baby my 150$ airbrush, but the 20$ starter ones in this set work fine with virtually everything. I still use one of them occasionally when just base coating because of how loose the tolerances are on them and how easy to clean they are. But yeah this kit is a fantastic place to start, costs less than most high end airbrushes and comes with a compressor too. If he has any modeling paint he can just add water and spray through these without issue.