Lately, I’ve been paying $100 a month for Fios. I’m thinking of canceling this service because I rarely use my internet at home, since I’m at school most of the time and my college offers internet (both Wi-Fi and grounded). However, I’d still like a way to do my online banking, which can take several hours, at times, for me to finish with. Apart from WiFi, where else may I go to perhaps rent out a cabin with a grounded Ethernet connection for a couple of hours throughout the week? I was considering simply going to an internet cafe, but how can I be sure these internet cafes won’t be sniffing or logging my personal data? Is my personal home internet, which is behind a wired router, really the safest route for the time being?
Unless you've installed extra root certs, your connection to the bank's site should be encrypted (though it's not a bad idea to explicitly type
https://[yourbank].com to avoid the potential for an sslstrip attack).
Even if you go to the
http:// page and someone does an sslstrip attack, most modern browsers will warn you when you try to type your password on an unencrypted page. It's possible sslstrip could be combined with a redirect to a homograph domain that the attacker has a certificate for, so it would be encrypted and could potentially fool you, but all of these problems are avoided if you go to the HTTPS site and carefully check the URL before logging in.
For the average person these days, the security of the device they use for online banking is much more of a concern than the connection to the banking site. If you have malware on the device you use for online banking, there's always the possibility that it can log your username and password.
There is no magic about wires versus wireless. Wired internet providers (especially in the US) have been known to sell data about their user's browsing habits and to insert tracking beacons in their user's web requests. So clearly you believe there's some benefit to wired internet that you don't get from wireless, but I'm not sure that's really true.
As the other answerer said, the security in https web pages (which is your banking and such) are almost certainly sufficient for your purposes. Going to a bank via https on a coffee shop's wifi is no less secure than going to the same bank via https at your school's wifi or wired connection.
You haven't really defined 'safe' so we don't know what you're trying to protect from. If it's the usual malware, spyware, and nasty stuff that anyone might bump into on the web, you'll do better to protect your web browser. Use an ad blocker of some kind. On MacOS I use software called "Better" (in the app store and available on iOS). In Firefox and Chrome you can use AdBlock Plus. The fact is that ads are the most pernicious trackers on the web, and advertising networks are how most malware gets transmitted to unsuspecting users.
Keeping yourself "safe" on the internet has nothing to do with preferring wired over wireless networks. It's much more about what protections you have on your laptop/phone/tablet and what sites you visit/use in your daily life.