Trade-in 5c

Apple doesn't take trade ins. They do have a recycling program. An iPhone 5c 32GB in perfect condition, that is not carrier locked, will net you $75 in Apple store credit.

As for buying on a 2 year contract, you'll have to contact your carrier about that. Most US carriers are doing away with subsidized phones on contract.

See http://www.apple.com/iphone/trade-up/

Looks like the best you can expect for a pristine condition iPhone 5c will be about $75. You will not know the actual credit until you take it in to an Apple store so they can evaluate its condition and place a trade up value on it (or ship it off to BrightStar on your own and get your store credit from them).

As to the cost of a new iPhone 6, again, that is available on the Apple Store site, or you can ask them at the store. Depending the device you pick, how much storage it has, and the carrier you wish to sign up with, your payment plan will vary (e.g. a 64Gb iPhone 6 with AT&T, payments over 24 months, will be $27.05 per month, plus your plan charges).

As mentioned, the carriers really no longer offer subsidized pricing. The do offer installment plans for the iPhone's retail price, and you can upgrade at various times by paying off the remainder and entering into another contract with a fresh installment plan. Whether you are eligible or not for an installment option will depend on your credit record and/or history with the carrier you wish to sign up with.