Start with the good news. You cannot buy the wrong one by mistake.
The YubiKey 5C NFC, the 5 NFC and the 5C Nano are the same key in three different shapes. They run the same firmware and support the same protocols: FIDO2 and WebAuthn for passkeys and security key sign-in, U2F for older services, smart card for certificate logon, OpenPGP, and stored authenticator codes through OATH. Nothing on that list is missing from one model and present in another.
So this is not a security decision. It is a decision about the hole you plug it into and where the key spends its life.
Question one: which port
Look at the machine you sign in on most.
If it has USB-C, which covers most laptops sold in the last several years and every current MacBook, you want a C model. That is the 5C NFC or the 5C Nano.
If it has USB-A, the older rectangular port still found on desktops, docks and plenty of office hardware, you want the 5 NFC.
Adapters exist and they work. They are also the thing that goes missing on the morning someone needs to sign in, so buying the connector you actually have is worth more than the few dollars it saves.
If you move between both, buy for the machine you use under pressure. That is usually the laptop.
Question two: do you sign in on a phone
This is what NFC is for, and it is the question people most often skip.
NFC lets you tap the key against a phone instead of plugging it in. Both iPhone and Android support this for security key sign-in. If any part of your working life happens on a phone, an authenticator prompt in a taxi or approving a payment from the warehouse floor, NFC turns a fiddly moment into a tap.
Two things worth knowing about it.
Almost no laptop or desktop has an NFC reader, so on a computer you are plugging the key in regardless. NFC is a phone feature, not a wireless upgrade for your desk.
And on iPhone, the connector question depends on the handset. Recent iPhones use USB-C, so a 5C NFC works either way, by tapping or by plugging in. Older iPhones use Lightning, where tapping is the only route a 5C NFC can take. That still works, it is just worth knowing before you assume you can plug in.
Question three: does it travel or stay put
The 5C Nano is built to disappear. It sits almost flush in a USB-C port and is designed to live in one machine permanently rather than ride around on a keyring.
That makes it excellent as the key that never moves and poor as the key you carry. There is very little to grip, so removing it regularly is a chore, and a key that protrudes a few millimetres from a laptop you throw in a bag is a key you will eventually snap off or lose without noticing.
The two NFC models are the opposite. They are keyring-shaped, they have a hole for a split ring, and they are meant to be handled.
The short answers
If you have a modern laptop and a phone, buy the 5C NFC. It is the model that suits the most people, which is why it is also the one most people search for.
If your main machine has USB-A ports, buy the 5 NFC. Same key, older connector.
If you want a key that lives permanently in a desktop or a docked machine and never leaves the building, buy the 5C Nano.
Where the Nano really earns its place
Everyone needs two keys. One key is a lockout waiting to happen, because account recovery without a second factor is the weakest part of the whole design and you will meet it on a bad day.
The usual pairing is an NFC model on your keyring and a Nano in the desktop at the office or at home. The travelling key does the daily work. The Nano is registered to the same accounts, sits in a machine you can always get to, and costs you nothing in pocket space.
If you would rather the backup lived in a safe than in a machine, a second NFC model is easier to hand to someone else in an emergency.
Things people get wrong
Buying one key. Covered above, and it is the mistake with the worst consequences.
Assuming NFC works with a computer. It generally does not.
Putting a Nano in a laptop that travels. It is not designed for that, and a key you cannot easily remove is also a key an opportunist can use if the laptop is left open.
Buying a C model because it sounds newer, then discovering the office fleet is USB-A. Check the port, not the year.