for a nas, both approaches would work
the thing is find the solution that will not make you open the case an unplug and plug back the cable constantly to make things work
what i would try is the ide to sata, is what most people use for long term usage, the converter to usb is meant more for data recovery, for external usage, not for constant usage
this looks nice
https://www.amazon.com/Generic-IDE-SATA-Adapter/dp/B000RK89M4
but you say you need 4 hard disks, so perhaps a pci express card with two ide adapters would be better
this one has only 1 ide ata port
https://www.amazon.com/QNINE-Controller-Expansion-Express-Convert/dp/B06WVD2BKD/ref=sr_1_2?s=electronics&ie=UTF8&qid=1499261629&sr=1-2&keywords=pci+express+ide+controller
but has other ports, also the ide ata port will suport 2 hard disks with one single ide cable so theoretically you need two of those cards, there is pci models too, in case your mainboard doesn't have enough pci express slots but has a old pci port
https://www.amazon.com/Sabrent-SBT-RDIT-Silicon-Image-Controller/dp/B0007LQKME/ref=sr_1_19?s=electronics&ie=UTF8&qid=1499262057&sr=1-19&keywords=pci+ide+controller
remember that the speed, the bottleneck will be thanks to the ide ata port in the hard disk, most of those old ide hard disks work at 30 or 40(hopefully) megabytes per second(the port limit is 133 megabytes per second but i never found a hard disk reaching anything over 50), basically at the speed of a usb 2.0 port, so forget any usb 3 hub to speed things up, the usb 3 hub will deliver usb 2 speeds because the hard disk itself is not faster to read or write