I've used the StarTech IDE -> CF adapter, works fine
I've used some IDE -> SD card adapter thing I found on eBay, works just fine
Now I'm using the StarTech IDE -> SATA adapter attached to a Promise Ultra 133 TX2 with an SSD (80 wire IDE, of course) and it works just fine, even prior to driver installation for the TX2 in Win98SE.
The CF and SD adapters didn't need any kind of extra drivers and just worked out of the box. The SD card adapter is basically the generic thing you find when searching "ide to sd card adapter" on eBay with a 3d printed 3.5" tray for it I also got on eBay.
The CF and SD cards, especially the latter, made moving files really easy and making backups of the OS is as simple as "pull drive, attach to main PC and run imageusb, compress resulting BIN file, dump on NAS". The SSD will most likely last longer since it has some amount of wear leveling and garbage collection at a firmware level, which the SD and CF do not. I've got it attached, but not screwed down, to this sabrent 2.5" to 3.5" tray thing so while it isn't as easy to remove as the CF or SD, I can still quickly yank it if I need to make a backup or swap a newly imaged SSD in there.
Just be aware a full-fledged SSD is going to be severely throttled by the UDMA/33 IDE speeds so the difference between it and an externally mounted SD (A2 rated) may not be as noticeable. I probably could've kept using the SD card I had, but I have a bunch of 120GB ADATA SSDs lying around without anything to use them for.
CF is the 'easiest' for these systems since any adapter is basically a dummy that passes the IDE connection through, but the cards can be expensive per GB compared to the SD/SSD. Might be that Amazon tax, but a few places I poked into sell them new for like $1 USD per GB
Whatever you chose, keep it 128GB or under as I've had my 440BX board throw a fit on some larger drives. Didn't matter my 240GB SSD was formatted in half, Win98 and FreeDOS didn't like it when run on the hardware, even through the Promise IDE card. Also grab some of those Molex to Berg cables, the CF and SD adapters I've used/seen use those for power and you might not have a spare one if you're also using a floppy drive. The StarTech IDE->SATA adapter comes with a power cable attached, so you don't need to worry about that one. The SD card adapter might need a longer IDE cable due to how it connects to the adapter, but YMMV depending on where it gets mounted and where the board's IDE ports are.
Win98+DOS: C3 Ezra-T 1.0AGHz / P3-S 1.26GHz, 128MB RAM, AWE64 + Orpheus + Audigy 2 ZS, Ti 4200, 128GB SD card
Win XP SP3: C2Q 9650, 4GB RAM, X-Fi Titanium, GTX 750
PowerMac G4 QS 800MHz + GeForce4 Ti4200, OS 9
PowerMac G5 DP 1.8Ghz + ATi x800 XT, Leopard