SegWit will not result in a chain split if it's implemented with a high amount of hashrate, which seems to be the most likely scenario right now.

Ideally, you'd be running a full node if there was a chain split.  Most of the major wallet providers will give instructions for what to do, such as Electrum's hard fork plan, and you should not keep coins on an exchange or online wallet.

Short term - panic and confusion about Bitcoin in the event of low consensus results in slight altcoin rises and Bitcoin falls as people move funds to altcoins as a "safe" haven.

Long term - Bitcoin rises dramatically because people start to believe its utility has improved.