As with any split, the general recommendation is to keep your funds in your own wallet, and not on some exchange, Localbitcoins, etc - if you have control of the private keys, then you will own coins at both sides of the split - if you own coins at some exchange, then it's totally up to the exchange to define what kind of bitcoins you have after the split.
That said, if an exchange promises to honor both branches, then it's most likely safe to keep funds at that exchange - like with the Bitcoin Cash split, those who kept their bitcoins at ViaBTC had a window of opportunity to trade Bitcoin Cash very early.
This split probably won't come with replay barriers. This means one has to actively split the coins to be able to control the Bitcoin Core coins and SegWit2X-coins separately. If having the coins at the right exchange, it's no need to worry about it, the exchange will take care of it.
It's a bit too early to give advises on what exchanges and wallets to use, or how to split the coins. The split will happen in November, not October, and still much is unknown.