This - and just so you can gage the "economy" of time and work involved as well -
If you get a sata gamestar adapter from Aliexpress (they dont have LAN ports on them), filling up a 1TB HDD via an external USB 2.0 adapter, takes about two days including - lets say "several minutes" to acquire every iso. I'm talking about "work days" (i.e. two 6-8 hour stints on two days on a weekend).
This should give you an idea how necessary it would be to get a Sata adapter with a LAN port on it. As in - not that necessary. Taking the HDD out everytime you'd want to add a new game is annoying, doing the entire setup in two days - is not.
Transfering from USB to the internal HDD on the PS2 is out of the question (write speeds slow as heck), adding Psone games using f.e. popstarter is done by adding them to the USB stick, so no interaction with the HDD anyhow.
So the most economical (time/money) setup that makes sense today is a fat PS2 with a FMCB memorycard from aliexpress, with a gamestar sata adapter from aliexpress -- and a used WD Mybook (or similar), where you can get the Sata HDD and the USB adapter (for the PC) in one swoop (dont buy Mybook NASes, just external hardrives (no LAN port on an external harddrive
)). If you need a USB HDD adapter.
Also think about maybe buying the 3D printed noctua fanmod ( https://gbatemp.net/threads/ps2-fat-quiet-fan-mod-w-noctua-fan.558129/
) as it really reduces the noiselevel by a lot (depends on your roomtreatment
), and PS2 controller extension cables from Aliexpress.
Thats all you need to get the best setup possible. All PC side software is compatible with USB HDD adapters, btw.
I'm personally very happy with a WD Red drive (5400 rpm) because it reduces the noise level even more (got one cheap), but thats not really necessary.