Yep, wallet security is paramount. A lot of the horror stories you hear in the crypto-space revolve around security measures that weren't up to par.
That said, the main types of wallets and what makes them unique:
Web-wallets (exchanges): easiest to use, most convenient in accessing your coins but most vulnerable for attack. With the web wallets your private keys, and essentially your coins, are not yours since the app or site are the one's truly holding them.
Desktop wallets: a step up from webwallets, they provide a level of convenience but ultimately in terms of security they are only as safe as the computer you're using. Some of these provide cold storage solutions though which is good. Electrum is a very popular software(desktop) wallet.
Hardware (external) wallets: Inherent cold storage solutions, as they always hold your coins offline (until you're ready to make a transaction) thus making them the most secure from potential malware. These are always a good option for storing large amounts of coins.
There's paper wallet options as well, which really just means having a printed copy of your private key on paper. This is regarded as highly secure as well since it's in your custody...just don't lose it. Ultimately why not have a couple? The perfect wallet combination depends on the person and managing them all is a skill that takes some time. Hardware is great for holding currency, but if you're trading, you'll also need something a little more convenient.
Cheers!
Yes, I agree with you. A combination of desktop wallet and paper wallet or hardware wallet may be the best option security-wise. Thanks!