Will a MetaMask wallet work for airdrops or should I only use MEW?
Any standard Ethereum address will work independently of the wallet, ledger or web that you use to generate it. Please be aware that exchange's addresses are not standard addresses and will most likely not accept any airdrop.
So, the answer is yes, if you create a new wallet with Metamask your public address will work to get airdops. Your public address will always start with "0x", never loose or give your private key to anyone.