If I want to use a smart contract, do I have to create a new currency/token, or can I do them using ethers?
If I can use ethers, what will be the consequences on the data stored and encapturing the execution of those smart contracts?
No need to create a token. That's just one potential use of a smart contract.
All Ethereum transactions are paid for with ether.
I can't understand what "what will be the consequences on the data stored and encapturing the execution of those smart contracts?" means. If you have more (specific) questions, please ask them.
As @smarx said, there's no need to create a token. I think people and companies create tokens because people seem to like earning/buying virtual points.
You can think of a smart contract like a computer software, which is executed not on a single computer or server, but by every ethereum node in the network. These smart contracts are written in such a way that for a certain state of the blockchain, the code has the same output.
So your smart contract can contain almost any business logic you need. The smart contracts for the tokens have a rather simple business logic coded into them: issue a certain number of tokens, keep track of what address what balance it holds, offer the possibility to transfer this balance between 2 addresses and that's kind of it.