Mikey, there are a few things I can tell you.
Don't go in looking for a payment. There's nothing a sales person wants to see more than a customer who wants to talk payment. I have friends who did that years ago after happy hour (derp). They walked out with a new civic. I looked at their payment and term....they easily could have walked out with a new Corvette with the payment they had.
Sales uses a 4 square system. The whole thing is designed to make you focus on the monthly payment. Don't do it. Tell them going in that you're paying cash and you have no trade. You want a price. Nothing more. Once you get to a price, say.....you know, I may want to trade my car after all. Why do you do that? Because then you'll know what they're actually giving you for the trade. When they come back with a trade number, you negotiate some more. They say 10 on the trade and (to make a number) 27 for the new car. It's not out of line to say....well, my car and 15 and I'll do it. Let them negotiate from there. (I'm just picking numbers) Don't be afraid to lowball. Know what your car's numbers are. My wife's car.....I was prepared to trade her old outback plus $13k. I threw the car plus $10k and they didn't blink. Came back with 10.9. I said ok, but they had to buy and install new snows. They agreed.
If you negotiate with a trade on a monthly payment, you are going to get screwed. Screwed, screwed, screwed.