I have 18" wheels and I'm thinking of going to 16".
I'm looking for a little softer ride and paying about $200 less for a set of smaller tires when they need to be replaced.

If I sell the 18s on Craigslist, what is a good asking price?
What is the going price for a set of used Mazda 16" OEM alloy wheels going for?
Will the steering response get very sloppy with 16" wheels or not make that much difference from the 18s?

 

I'm not able to opine on questions one and two, however, question three is pretty easy to comment on. Yes, your steering response will become noticabley sloppier if you go all of the way down to sixteen inch wheels. While I agree with you that eighteen inch wheel and tire setups aren't optimal for much of anything, were I in your shoes I'd buy a seventeen inch setup. Why (relative to your current setup)? Possibly better steering response, lower cost for tires, better rim protection when encountering pot-holes and the like.

When you compare a sixteen inch setup to a seventeen inch setup, you get more of a mixed bag:
- Steering response: Advantage 17"
- Tire cost: Advantage 16"
- Pot hole protection: Advantage 16"

 

I found a set of 16" RX-8 wheels, going with these.

 

What size of tire are you going to put on those rims?

 

Tires on the 16s will be, 205/60, 215/55 or 225/55 depending on price and availability.
I may go with a cheap set of used tires just to see if I can live with decreased steering response before getting new tires. The 16s have a lot of sidewall to live with compared to my original OEM 215/45/18s. I have two Miatas, '99 Sport/Hard-S and '00 base, so 16/60 series tires on the 6 may feel like a boat.