It depends on what you really mean by "cheapest" for one. There's cheaper than buying a flagship/major manufacturer for $600+ over 2 yrs. and there's buying a $50 go-phone from Walmart with Android 4.3 and 5MP camera.
When upgrades stopped being free or significantly discounted and the carriers just put you on financing for 2 yrs, my wife and I stopped doing it and went to Craigslist/Ebay or unlocked phones. It is definitely much cheaper if you don't mind not having the latest and greatest and don't mind a little risk (CL/EB) and paying a little more up front.
Absolute cheapest is probably CL, but you risk stolen devices or devices with hidden hardware issues or issues associated with "hacking" or modification with third party software. EB at least offers a layer of protection in that EB will provide support if the device is not as described, etc. but you still have the same risks.
Probably the best option is to buy unlocked from a reputable dealer (Amazon, Best Buy, Walmart, Motorola direct, etc.). Then you know you get a new product and have manufacturer's warranty, 30 day return, etc.
As getme pointed out, Motorola is basically killing it in this market right now, giving probably the best bang for buck in the $200-300 price range.
Some majors like Samsung have also entered the budget unlocked phone market, like Samsung's Galaxy J7 Pro. There are also lesser known companies making decent to really solid unlocked phones though, like Huawei, Blu, ZTE.
I just got a Huawei Honor 6x on a now-expired deal for $100 (it's $180 normal retail, but I'd watch Black Friday) and this thing would blow your S5 out of the water. I think I'll add more to my review on the
thread that linked me here. since I mentioned it there first.
EDIT to add: If you do try Craigslist/Ebay, always ask the seller for the IMEI prior to bidding/purchasing and clear it with your carrier to ensure you can activate the phone once you get it.
