That's right, Verizon phones don't use SIM cards. The iPhone 4s (and I think the 4) does have a SIM slot because it can be used on either CDMA or GSM, but you don't use that for Tracfone's BYOP. The phone does need to have been previously on Verizon, and be unlocked.
I've done this twice with a used 4s each time, buying one from eBay & one from Amazon. It costs $10 to register each phone with Tracfone. On eBay I get 200 minute cards for $32 that triple to 600 voice minutes, 600 texts, and 600 MB of data for 90 days. It's great for moderate use, especially if you're on wi-fi a lot and you use Apple's iMessage feature for some of your texting. I also use YouMail for voice mail, which avoids Tracfone's clumsy voice mail that charges you for both your calls to listen AND your callers' time leaving messages.
There's a lot of useful information in the comments here, including links to even cheaper airtime:
I think it's wise to the extra $$ to get the iPhone 4s over the 4, for its extra speed and capabilities. Ours run iOS 7 pretty well (although I haven't spoiled myself by trying a 5s).