store coin in wallets like coinbase or blockchain.
Never store ur coins in online wallets. Online wallet turn off website/service, u lost bitcoins.
Use software wallets or paper wallets etc.
About topic question, in case of hardfork, safest is to not move ur coins at all. Wait to things to settle itself.
If they're in an online wallet now, the best option is still to move them. Online wallets are likely to take one part of the forked coin, just like how Coinbase took its users' ETC.
Downloading Bitcoin Core will be pretty demanding, so as long as you're not an idiot (or very unlucky person) that gets loads of malware you'll be best off holding it in a software wallet. Download Electrum or maybe Multibit and you'll have control of your coins.
You shouldn't worry until a hard fork is imminent though, and right now it's not.
