Now that I have one Bitcoin, I need to cherish it.
As far as I understand, you were aimed at gaining 1 BTC from trading, and finally you have achieved this goal. Congratulations!
By the way, you do not need to cherish Bitcoin. This is just part of your finance.
My next move will be transferring it from an exchange to a cold wallet (Ledger, perhaps?)
Yes, Ledger is a safe and secure hardware wallet that supports Bitcoin and other cryptocurrencies. Your next step may be quite difficult. As people say: "Not your keys, not your coins".
Sell some junk you have laying around on eBay. Put $20 per paycheck into Bitcoin. Move $1000 from your savings into Bitcoin. Get started, and enjoy the ride.
Since the price of Bitcoin is volatile, some unexperienced newcomers can be disappointed by this "ride". So what about gain yet another 1 BTC? You looks as a skilled trader, so I advice you to continue to trade, using your successful strategy.