Pro-tip: Go for a Ledger Nano S (https://www.ledgerwallet.com/products/12-ledger-nano-s), it is (IMO) the best hardware wallet available. Had a terrific experience using it, it is a genuinely great product.
1. Pick a high-profile exchange
Pro-tip: I had an absolutely terrible experience with Coinbase. And a far better one with GEMINI (Although I have issues that are +30 days old still open with their customer support. I'm pretty disappointed).
2. Get your account verified (KYC)
Pro-tip: If you are concerned about your privacy, you can always buy bitcoin for cash on localbitcoins. They have an escrow system.
3. Purchase cryptocurrency of your choosing.
Pro-tip: look at historical charts (both Linear/Log scales) and do your best to "time" your order, of course it is hard.
4. Move back funds to your hardware wallet.
Pro-tip: Whatever HW wallet you choose, do not leave your funds on the exchange. Just don't do it, accounts get hacked all the time (even with 2FA), exchanges get hacked all the time, remember MtGox and learn from others' mistakes.