Does your computer have a Make and Model or is it just a Whitebox? What is the Graphics Card?
I have 2 Dell C400 laptops which have problems because of the Intel video. The distro that works best for me, out-of-the-box, is Aptosid. I am fairly sure that their kernel is based on Liquorix.
As a former Debian Sid user, I used aptosid when it was called sidux. Many users switch to using the Liquorix kernel because of restrictions incorporated into the default aptosid kernel. BTW - if you mention Liquorix in their forums or on IRC you'll get a response similar to bumping into a beehive. Just an FYI.
As for the topic, it seems like you have a much older computer which restricts your choice of distro, especially if your looking for speed. AntiX, which is a spin-off of Mepis does well on older computers. Link below:
There's also Puppy, which just had a release today, link below: