I'm aware that you didn't suggest using a flash drive.
For an inexperienced user it may be easier and cheaper to simply buy a self-contained USB pen drive (a.k.a. "flash drive") to plug in to a USB port, rather than buying a hard drive and an external enclosure to put it in.
Some enclosures are expensive, as are some hard disks. And installing a hard disk in an enclosure can be as technically complicated as installing it on the IDE cables. Buying an enclosure that already contains a hard disk is not always practicable if the enclosure is to be used with Windows 98: they typically come formatted as NTFS, which Win98 can't read from or write to; and the hard disk is typically 500GB, which is way too large to use with Win98, which can't use a partition that exceeds 125 GB.
Buying and fitting a special cable is technically less demanding than installing a hard disk. And these cables always come with the necessary software supplied. All that is needed is to buy one which has software for Windows 98. Laplink 2000, for example, is a transfer program that will work with Win98.
These cables typically come with a variety of connectors, e.g. for USB, parallel ports, and serial ports. This gives additional flexibility, and may avoid the need to use USB at all. A parallel port transfer will be slow, but not much slower than using USB 1.1 (USB 2.0 is pretty uncommon on Win98 machines).
If the Win98 computer can't boot to Windows, but can boot to DOS, a file transfer can still be done by cable, using the DOS program Interlink. I've actually used a Laplink 2000 cable to do such a transfer, using the parallel ports, running Interlink for DOS instead of the Laplink software the cable came with, because Windows wouldn't start.
The poster forgot to mention whether the other computer had IDE connectors, or whether the intention is to use an IDE adapter; but it will not make a great deal of difference. A bi-directional IDE/SATA adapter will cost about $25.
If the other computer uses IDE, the simplest procedure is to jumper both of the hard disks involved to "cable select", as this removes one unneeded complication.
Leaving the jumpers off, so that both disks default to master, is superficially simpler. But that requires the novice user to attach them to seperate IDE cables, which means detaching the DVD-ROM drive: that can be difficult to re-attach, with its extra connector, if you've not done it before. It adds at least one extra complication, so is best avoided.