The KLH 20 is a turntable and tuner with separate speakers. It was an early example of a "plug and play system" (of course that terminology didn't yet exist) and It is capable of quite good sound. The rest of the stuff is extraneous (the Mission speaker is good, but it seems as if you only have one, and about those Criterion speakers, the less said, the better). IMO it's definitely worthwhile to get the 20 working if you have any use for a vinyl or FM setup. Also, it looks like there are AUX and Tape inputs, so you can plug in a Bluetooth receiver and/or CD player (all output the same sort of signals, so they're compatible with both Aux and Tape).
Back when this system was sold, getting a good hifi system was complicated. You could buy a complete console, which required no setup, but sound quality was all over the place and it took up lots of space. On the other end were separate systems which were relatively complicated (for people whose only exposure to technology was plugging in a toaster) and required some help to select the components. This was a relatively early "compact" system, which made it easy for someone with no audio experience to purchase and set up. Later compact systems had a similar idea, but sound quality usually suffered. When you purchased a KLH 20, you simply plugged the system into an electrical outlet, then plugged one end of a speaker wire into the speaker jacks on the rear of the turntable (technically it's a turntable plus receiver, but I'll continue to call it a turntable for brevity), the other end into each speaker, and you were done. From pictures I've found online (I've never owned one of these), the KLH 20 turntable used RCA jacks in the back of the turntable, while the 20 Plus used binding posts. While yours is clearly labeled Twenty, you should check in the back of the turntable to see what sort of connectors the speakers use, as it's possible that they changed the connection type during the manufacture run.
In any case, all you need are a pair of RCA speaker cables (or if you have RCA jacks on the back of the turntable, RCA to RC.A). The former are
easy to find, the latter not so much; in fact, I was unable to find any RCA to RCA speaker cables at all (Radio Shack used to sell them, but we all know what happened to
them). There are plenty of RCA to RCA subwoofer cables, but these are less than ideal for speaker level signals. Assuming you have some extra wire lying around, I'd get a set of
these (you'll have one left over) and make the cables myself.
Now, you didn't give us any indication as to your tech skills. One well known issue with KLH speakers (and indeed most speakers from this era) is for the capacitors inside to fail, which will significantly reduce or completely eliminate the high frequency output. Replacing the capacitors is relatively straightforward but it will require removal of the woofers and some soldering. Searching for
replace capacitors klh speakers should give you lots of useful info.
