For a long term, you can buy on the exchange that have low price, store into safe wallet and sell on the exchange that have high price (in this case you use 2 exchange to do a trade, but long term), you can use this site:
https://bitcoinaverage.com/en/currency-markets/btc-to-usd to do a comparison.
For a short term, you should consider the volume too and keep in touch with the news, if you can read the chart it's better.
About storage, just use a stable hardware wallet such as Trezor or Electrum and make sure you use a strong password and other security measures like 2FA.
Also, how can I be sure that Trezor or Electrum won't "do a MtGox" and have my Bitcoins disappear?
Trezor is hardware wallet, electrum is lightweight wallet and mt.gox is the exchange. Those all is different thing, with trezor and electrum you hold private key of your wallet, so nobody can steal your btc, unless your device/PC infected by the virus/malware/malicious thing which can hack/steal your coin, so you need to careful while browsing/do internet activity.