Note: If you have a cheap prepaid plan, switching to a major carrier just for a "free" phone usually costs you more in monthly fees over time.
Carriers like Verizon or AT&T often offer "free" phones with a trade-in. This is only the "cheapest" way if:
The sweet spot for value is a phone that is exactly two generations old. For example, when the iPhone 16 drops, the iPhone 14 hits its peak price-to-performance ratio. You still get modern software support and great cameras without the "new release" tax.
If you must buy brand new, wait for these three windows: Black Friday: The best time for unlocked Android devices.