You should use IDEX with MetaMask or hardware wallet. Download MetaMask from https://metamask.io. Import your seed locally and make sure there's no malware lurking around in your computer.
On another note, I don't think you can buy Chainlink with USD directly from IDEX. Another option for you is to use an app like Abra to buy Ethereum/Bitcoin with your credit/debit card and then transfer it to your MetaMask account to buy LINK from IDEX. You can also use Coinbase to do that, but it will require KYC.