Grindcore is tricky because it's very easy to just be noisy and childish for the sake of it, but here are three albums that are great introductions to grindcore:
Nasum- Inhale/Exhale
Carcass- Symphonies of Sickness
Napalm Death- Death By Manipulation (this is a compilation of various EPs they'd put out up through 1990 or 1991, and it shows both their 'old style' and 'new style [for that time], but has much better production than the earlier Scum and From Enslavement to Obliteration albums where most of the songs first appeared)...