As above there are often 20 gig models in second hand game shops going for a pittance (more than it costing them to scrap after all) that you might be able to find one of the replacement drive models for* and do the whole hdss.bin dance. Indeed here is me in 2012 https://gbatemp.net/threads/uk-gamestations-360-20-gig-hard-drives-for-a-fiver.323257/ . I have also seen places get rid of RRoD units with them still attached as well.
*naturally JTAG and RGH don't care here. Stock or only DVD modded stuff will need either originals or those handful of models that were rare at the time and bought up by 360 owners of all stripes.
A handful of third party replacements of the shell/holder/clip on/caddy/... did appear on the market at one point (some looking like stock, others more fancy), the usual (re)sellers of random Chinese plastic goods and what few modding device websites still around from then being where you might care to go for that one.
USB drives, even on stock models, did become a worthwhile concept towards the end too.
I was just going to post... why in the world would anyone recommend a 20GB drive when the above is possible. I believe you can use WD VelociRaptor Series as well, but I personally used a 250GB Scorpio back when I had a 360.
ebay may be a good place to get caddies. I have a pink, transparent one for my jtag. I also have a green, blue, and gold transparent ones. I would periodically change the hdd caddie color, but I've left it pink for about 10 years now. the caddies are just generic, only the hdd is important.
i believe 500GB is the max now for stock 360 using HDSS.bin but for stock systems USB storage would be fine for most if those older Scorpio drives are hard to find now and even a 20GB is good enough to enable original Xbox BC.
I got the one I'm using in my RGH'd console now from the Gamestop by my house for $10. They tend not to sell them on the site, but if you have a local store, stop in and look around, they're usually in these weird little ziplock-style bags.