You can do either method.
Take up less file space.
Files are already cut.
Long continuous shot
Easier method when shooting, but more work in post.
Easier to sync a continuous audio stream such as from an external mic.
The artifacts are on the original footage because a DVD used some oldie MP2 codec, you need to live with it.
You could try using a denoiser, some of them can detect compression artifacts. I am not spamming or anything, but take a look at Neat Video Denoiser.