I have the 32 GB 5s, and could manage on 16 GB. The primary issue would be if you store media files on your phone, or if you use gaming apps. If you use a 16 GB phone, you'll have to keep a tight watch over the storage, because things like app and system caches can pare down the capacity in a hurry. Games are especially bad at gobbling up huge chunks of storage as you play more. You might have to periodically restore your phone as new, and then reload your apps and settings from a backup, in order to flush out the caches and junk data and keep the storage usable. As the phone gets close to capacity, the performance can noticeably deteriorate.
$200 is a subsidized price. The costs are hidden, so you pay more in the long run. You're paying for it every month with higher priced plans, and it forces you into a two-year upgrade cycle, because when the contract's up, your monthly rate does not go down.
Buying off-contract lets you pick and choose from different carriers and plans, and you can switch whenever you want. If you'd locked yourself into a contract two years ago, you would have missed out on all the new plan options and cost savings that opened up after T-Mobile got rid of contracts. The cost savings on the new plans would more than pay for the cost difference in buying the phone off-contract.
I paid $750 for my 32 GB 5s in September 2013. It's $450 more than the subsidized $300 charge. But, I use T-Mobile's $30 prepaid plan, so I'm saving more than $60 a month compared to the contract options that AT&T and Verizon were offering at that time for the amount of data that I use. The contract-free phone paid for itself in less than 8 months.
And since that time, all of the major carriers have introduced new contract-free options, and device upgrade plans that separate the device cost from the monthly plan. Do the math. Contract-free is the way to go.