You should definetly store your Bitcoins on a wallet which you have full control over.
I would not recommend to use an online wallet. Thats the only way to ensure you will own both coins after the fork.
Once the fork appears there are 2 coins which share the same block history (until "fork-block").
This means for every BTC you own, "you will get" one forked coin (simply by still owning the private key which has value at the time of the fork).
But there is no guarantee for you to get your forked coin from web wallet provider.
Electrum is a nice light weight wallet (does not download full blockchain).