The four models are really four answers to one question: who eats it when the list is bad.
Per caller hour puts that on the investor. You bill for labor, they own list quality, script, and follow-up. It's the easiest model to deliver and the hardest to sell, because the buyer has no idea what an hour buys until they've bought fifty of them.
Per lead moves the risk onto you. You only get paid when a conversation clears a definition, so a weak list eats your margin directly. That's why per-lead shops care so much about the list and often insist on pulling it themselves. Per appointment is the same trade, further down the funnel, priced higher because more of what you produce is unbillable.
Setup fees exist because the data really does cost money up front. Skip tracing is priced per record, often in cents, and a 20,000 record pull turns into a real invoice before anyone dials. Charging for it separately keeps you from financing someone else's list.
The piece that decides your model is your own cost per contact. Track dials per live owner conversation, then contacts per lead. Once you know those two numbers you can price any of the four models off the same math and see which one still pays you at your actual contact rate.
One thing to settle before you take a dollar: whether what your callers say crosses into brokerage activity where you operate. Discussing price and terms on someone else's behalf can trigger licensing depending on the state, and a real estate attorney in your state should look at your script before it's live.