Where should I securely store my coins during the fork? A Legacy address or a Segwit address? I keep them on a Segwit address right now but I want to be sure that the fork won't affect my funds if kept on a Segwit address during the split.
Because the Segwit2x fork has Segwit activated already and they are not disabling segwit, you can store your Bitcoin with any address that you want. You will be able to spend your coins on both sides of the fork regardless as neither Legacy addresses nor Segwit addresses will become invalid nor spendable by anyone.