Please recommend me some Punisher comics/graphic novels

Read the Garth Ennis Punisher Max series. You can pick up the trades at your local comic shop. IMO, the best Punisher run to date. I may be wrong but I think the series continued after Ennis departure but the quality dropped off a bit. It's been a while so I may not be remembering that correctly.

Stay away from the Max series. Pick up Greg Rucka run and to a lesser extent Nathan edmondson run. Both capture what makes the character great.

Max series turned him into a Dexter like character only he uses guns.

Definitely pick up Punisher: Year One by Dan Abnett and Andy Lanning, Also anything by Chuck Dixon and John Romita Jr. They were a bit more modern in their work with the character than the other writers of the 80's. But Carl Potts work is great as well, very serialized but well written and very informative on what you've seen in Season 2, like Schoonover. Also you can't go wrong with Steven Grant's work. Circle of Blood is an eternal classic among Punisher Stories.

The entire MAX run.

Punisher MAX up to issue 60 I think. Amazing stuff. Really brutal.

Punisher MAX Born. Good detail on Frank's transition to The Punisher in Vietnam. Probably one of the best Punisher stories.

There's a few one shots too. The Tyger, The Cell, The End. Can't remember what they're like though.

I'd just follow Bernthal's advice and grab anything I can find on the character. Then I'll decide which of it I find particularly exceptional.

Going with the classic and best well-reviewed ones is preferable to me, but acquiring whatever you can get is not a bad way to start. :)

Disappointed no one has recommended the Marvel Knights Punisher...it's tamer than the MAX series, but still good, solid, well-written Punisher action.

The entire Ennis rum was just reprinted in Omnibus format. It's amazing,both in story and quality of the book. You should be able to get in for about $60.