Just a few suggestions.
If you have the knowhow, build your own kernel from source. Cut out everything you do not need. If nothing else this will improve response times, and most likely memory usesge.
Use a light DE. LXQT and the DE from Puppy Linux (Can't remember the names) are two of the lightest you can find. The desktop tends to make the biggest impact on memory usesge.
Shop web browsers. There are a few that are super light weight that can significantly impact ram usesge. I can't offer insight into this except to say shop the alternative options because I've never had a reason to worry about it myself.
These steps in conjunction with a healthy swap file will assist in use ability. Sadly, even the lighter distros nowadays have shifted to a 2 gig minimum so 1 gig is stretching the limit. You would almost need to use some kernel and software stuff from over a decade ago to reach your goal, short of compiling your own shit from scratch. It's why people do suggest light distros like Tiny or Puppy. They already did the heavy lifting to get people closer to the goal
If you have the knowhow, build your own kernel from source.
I've never built my own kernel, I guess that'd weeks to learn well if not longer. I might be able try a different distro though, but then my scripts and stuff probably has to be adapted to that distro.
Check Gentoo docs. That masochist distro makes you compile everything from source so that would probably be a good start, if your serious. I don't know that it's worth the effort, but good on ya if your gonna try
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