Computer banking is not just a little, but statistically and objectively an order of magnitude safer than using your debit card (easy to skim), cash (good way to get a gun in your face) or checks (people clone these). Just use non-human readable password (scrambled ones) that machines can't easily crack along with a popular password manager like LastPass. And the bank phone apps on iPhone are even better as you can log in with your biometrics. Also, aren't most pumps tap to pay now?
Just remember than your bank or the IRS won't call you, they will send you official mail. Don't share a 2-factor code (that they give you over the phone) with somebody who called you, only if you called into their official number. Inlaws almost fell for that one. Also be careful on marketplaces like FB. And keep an eye on elderly and those with degraded mental capacities; they are the ones who are targeted (happened to my mom over facebook).