Here's a video of Accushift shifters with a regular Suntour FW using a Shimano chain.

I've got Superbe shifters with AP (Accushift Plus) 7 speed and a Cyclone 7000 RD (pic below), but it hangs on the upshift occasionally, if I'm not careful. (make sure your clicks are concise) I think AP was arrested in mid-development and Suntour didn't get around to beveling and ramping all the parts due to Shimano's patents. The upshift issue is probably due to the AP chain, which is not beveled at all - compared to SRAM or HG. I would at least try to pair the RD and the shifters, since adjusting these things (SIS and AP) is touchy enough as it is. As for the cable and housing, I settled for SIS, because the prices for those little details are even more inflated in the used/NOS market. I still prefer Suntour designs from the same era however, the Superbe/Sprint/Cyclone lines were lighter and more elegant in my totally biased opinion.