What is the cheapest way to get the iphone 6 plus?

What carrier is cheaper? I'm willing to consider new and used options

You are likely better off going with which carrier has the best service where you need to use the phone and the best plan for you.
You might want to keep an eye on promotions, it seems you just missed Sprints any trade-in gets $200 promo but it looks like Target might have a $100 gift card with activation promo.
Since I switched to Cricket to use my Oneplus phone I bought an unlocked iphone 6 for my wife. I was lucky to have a relative who works at an Apple Store and got a Friends and Family discount but did have to wait until he wasn't busy with other customers to have him order my phone. I did pay the extra for the Apple Care and to get the 64 gig.
You can get them for as little as $0 down but you will actually pay more than if you pay the roughly a thousand dollars upfront in the extra monthly payments.
The latest Apple and Samsung phones tend to have the same price everywhere so the cheapest way to buy and iphone 6 Plus it to wait for the iphone 8 plus to come out.
Used and refurbished is great if you can trust who sells it to you. I have heard good things about reconditioned products sold through apple but didn't currently see any phones listed on their website.
You might want to ask the apple store if there are any promotions that apply to you.

Maybe there will be some available when the next iphone is released? At&t and veriz are the best carriers, but tmobile, sprint and straight talk are cheaper (and slower).