Ah, the Altos systems. 8800 series, then 486, then 586. They used up numbers years before Intel got to them (the Altos 486 had an Intel 80186 in it, and 4 serial ports). Often paired with Wyse terminals. Anybody else remember "business basic"?
It's almost certainly an ST506 drive; you will be very hard pressed to connect it to a PCI era system; probably can only get as far as AT bus machine.
In any case, if you do manage to image the drive, the filesystem will be based on either Unix version 7, Unix System V, or the Berkeley Fast File System. It wasn't until Linux rolled along that we started to seriously fork into lots of file system variants. It's most likely the basic System V file system, which is well documented, and pretty simple stuff.
The posters above are correct, however. You really should try the serial port approach first. I'd go for cu over uucp - getting uucp running can be quite an exercise in itself. And you'll want either tar or cpio; probably tar, but watchout for version and format incompatibilities there as well.
You can also just cat the data out a serial port, and capture it as a session log on the other end. That's likely to be the easiest solution, and perhaps more reliable than any other.
You haven't said what the nature of the data is, but after this much time laying dormant, you are likely to have substantial challenges at the application level interpreting the data as well.