As others have said, there's no need to spend the extra money on a high-end airbrush manufacturer's compressor. I've had this one for a little over 5 years, airbrushing almost everything (I even got to the point where I mask and airbrush individual dials on instrument panels), and it has been very reliable:
https://www.amazon.com/gp/product/B006ACB6D2/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1
I'm considering getting an air tank and filling/refilling it with nitrogen as an alternative. I have pretty easy access to compressed nitrogen for a nominal fee, and it might be nice to go completely noise-free. Just like CO2, its also a completely dry gas.
Also, I know you already have the Iwata HP-CS in mind, but for a good first airbrush, I would also recommend having a look at the Paasche H model. I have used the same Paasche H for about 35 years and only recently tried an Iwata HP-CS. Frankly, I found the whole flushing/cleaning process on the HP-CS to be a PITA, and haven't found any situation yet where my Paasche H couldn't do the same job. Cleaning is really easy, as it is external mix, so every part that paint touches easily comes off the airbrush with a single tool. I drop all of those parts into a jar of MEK and run them in an ultrasonic cleaner between each color for a complete cleaning. An air cap, needle, and color cup set are fairly cheap (around 10 bucks), so I have 3 sets, which allows me to keep painting the next color while the previous color's parts sit in the cleaner. I like to call it the AK-47 of airbrushes...can't break it...can't jam it...it just keeps right on shooting.