I have a 1996 Toyota Starlet with the 4E-FE engine with 40,000 miles on it. The engine rattles when first started but almost stop on about 2-4 minutes after. Can any one advice me on this

What brand oil filter are you using?

I'm using a napa brand but i've tried other brand before. I think i'll try a thinner oil like 10/30 instead of 20/50 and see what happen.
I thought it was a loose valve rocker arm but when the cover was removed i realized it was haydraulic lifters.