Do any browsers try https first yet?
Now that I think of it, I guess many search engines now use HTTPS with HSTS and will send you straight to the https site if it knows of one, so that’s good.
This works for most things - for a few things I'll open an incognito window in Chrome, which simultaneously turns off extensions and doesn't send my original cookies, and I'll be careful about what I do in that window (certainly no logins to sites I care about). This is generally enough for e.g. reading some random news site that doesn't support HTTPS at all.
The reason I ask is, I'm under the impression that a VPN definitively mitigates this kind of attack. I'd have to change my habits if it turns out a VPN is not a one-stop-shop solution for this kind of attack. And, in case convenience matters to you: an enabled-by-default VPN is also less configuration and fewer manual steps than turning on HTTPS everywhere and blocking all unencrypted requests.
For performance reasons I don't want an always-on VPN; I trust my home wifi, my phone's hotspot, etc. at least as much as I trust any VPN I could use, so I wouldn't get any benefit from it.
I suppose the thing I should actually do is route over an SSH SOCKS tunnel to some server I control, which would work fine.
(A thing I have wanted for a while is a configuration that does this for HTTP and lets HTTPS through normally for performance, which now that I think about it, I can probably just write a proxy PAC file to do ... thanks, I'll see if I can improve my setup.)
This is what I do. The only danger with that over a regular VPN is anything not part of your browsers standard stream will not be sent over the proxy. This includes browser plugins as well. Thankfully Flash and Java are generally disabled by default, but it's still worth baring that limitation in mind.
Despite this, SSH SOCKS is still my preferred method as well.
The only other things that should be making connections are OS update checks, which should be secure already, and an SSH or mosh client.