You forgot one good and simple option CrocoDuck. The one i gave and have myself.
Buy an analog mixer board which can handle guitar amp (even when distorted) and has a master out volume. Most good older mixer boards have at least one channel for guitar amp.
Plug the mixer board in the soundcard.
Plug the guitar in the amp, and the amp in the mixer board (or w/ mic).
Done. As simple as that.
And plug in whatever more you want on the other channels (keyboards, mic's etc) just because you can. Or two guitars+amps together like i do sometimes when jamming.
My board is next to pc plugged in on an amplifier too. So i can record, or jam with others while mixing the jam. And if the jam sounds good i just have to push the rec button. A full studio setup IMO.
This jam setup for playing together was my goal for the several musicians in the house overhere. And only after that the experental idea came to plug in on a linux pc with recording facilities. And worked great so kept this total setup.
The fun is that everybody say's it's almost unreachable to record an amp distorted guitar ..... like i do ll the time.
I even know many who serious invested in gear and software who quit trying. Once was on a guitar forum and all said that my setup "can not work, or at least not propper". And "no latency problems" at all was reason to almost kill me. Man, got me big arguments when i kept saying "the impossible" that it worked perfectly
And one i know well his eyes popped out
when he actually saw my cheap setup working perfect.
Even better .... i can plug in EVERY electric instrument to jam or record it. Do that all the time.
That's why it is a mystery to me why almost everyone rejects this fine option quickly and grabs back at digital solutions that often appear to work not easily or even not at all. But after this reaction i'll stop promoting it.
Good older analog mixer boards with 8 or 16 channels many times are sold under $100 (test before buying!!). Where older doesn't mean worst, as the electronics were stronger/stabler that day's.