Need more details about what you're doing, but there's a very wide range of audio interfaces that can do what you (probably) need here, from Presonus, Focusrite, and Mark of the Unicorn mid-level units at ~ $300 up, to Apogee and Avid interfaces costing $6-7K. I'd recommend browsing computer audio interfaces at
Sweetwater Sound to get some sense of features and price range. Run your playback machine's outputs into the interface (you might need preamps depending on the analog machine's output levels), and digitize into digital audio software on your computer. Store in uncompressed WAV and AIFF formats, keep copies cloned on multiple drives. (Long term archiving in the digital realm is risky, but saving multiple copies in multiple formats and multiple locations offers some insurance.)
Actually, the audio interface side of this *should* be easy. Assuming your source material is analog tape, the tape and the playback machine will be the bottlenecks in quality. If you don't have studio experience with tape, it's probably worth hiring someone with experience and gear to comb through your deck—cleaning and realigning the heads, checking bias, checking the spool brakes, etc.
If you're working with older reels that are shedding, the tapes themselves are likely to need some restoration before you can play them for digitization. There are several schools of thought: baking tapes, using isopropyl, and restorative cleaning under controlled temperature and humidity. These methods are all somewhat destructive, intended to reduce shedding in order to render the tape playable for archiving. If your tapes are historically significant, consider consulting an archivist. The National Academies' reference
Preservation of Historical Records is a useful starting point (jump to p. 61 for the section on magnetic recording media). But if you're holding the master tapes to
Kind of Blue, please don't consider this a DIY project.