I had an Aspire One D270 laptop with a 32-bit Intel Atom CPU and 1 gigabyte of RAM, so I installed Debian with Xfce on it, but even then it's running way too slow.
Is there anything I can do to make the laptop faster and more responsive given its limited memory?
Do not run Slitaz as is fully of security problems and vulnerabilities. What's worse is that there website has security holes on it. There is a page on the bug tracker that runs arbitrary JavaScript and prints out the time as an example. It also has been abandoned and is no longer maintained all that well.
1gb of ram is quiet a bit. I've ran Debian Xfce4 on simular hardware it it works with a few tabs. The problem is the modern internet is graphics heavy and the old GPU doesn't have a lot of power. If you don't block ads with Ublock origin it will grind to a halt as the video and image rendering will be done by the CPU as the GPU is to old.
Because it isn't going to be faster to use something else else. Unless they added a ton of stuff it shouldn't use more than a quarter of the ram. Firefox suspends tabs under ram pressure so that shouldn't be an issue either.
I've done work on a old Atom with 1gb of ram. It isn't fast but it gets the job done. You can't just make old hardware run fast by changing the desktop