Whee, now that brings back memories. I had a small network of DN3500 Apollos back in the day. They are Unix workstations, running Apollo's Domain/OS, which can be an Apollo AEGIS machine, a SVR3 machine, or a 4.3BSD machine, depending upon environment variables set when you log in. The 3500's were 68030 boxen running at 25MHz with up to 32MB of RAM. The native hard disk controller on mine was a WD7000V-ASE ESDI and SCSI combo (totally unusable on a PC, incidentally). The SCSI was used for the DC600 QIC tape drive, ESDI for the hard disks. The slots in the 3500 were ISA, but very few ISA cards worked with Domain/OS, the notable exception being the 3Com 3C505 16-bit Etherlink board.
The Apollo FAQ is still up; one mirror is
http://web.mit.edu/kolya/www/csa-faq.html
Looking at your photo, I see you have the SCSI QIC DC600 tape drive, which is good, as the OS media is on DC600 or DC6150 cartridges, if you can find it from someone anymore. You'll want Domain/OS SR10.4 for that beast. The GUI can run X11, but the native GUI is not X. I don't have any media left over as far as I know, but if I were to find it I'll let you know (just don't hold your breath; it's been 24 years since I divested myself of those DN3500s). Did you get a keyboard? I might actually have one of those lying around, but, again, don't hold your breath, because if I do have one it will be buried, and might be difficult to find. It's a special keyboard. I think you can run headless with a serial console, though, but I'm really testing my memory on that! Of all the Unix systems I've owned, I ran the Apollos the least, since compatibility with other Unix wasn't terribly great, due to the proprietary Domain/OS GUI instead of X11.