Perfect! I'm going to second this one.1. Action - Superman is iconic, and this is the best Superman title in addition to being a good introduction to the character.
2. Batman - Batman is iconic, and while this isn't an origin story, Batman's character is iconic enough that probably doesn't matter and the book is quality and creepy. Hopefully it'd be a good introduction to the wider Batverse and supporting characters.
3. Wonder Woman - Again, the final member of the trinity but also it's just a kickass book right now - great art, great story, and a different, darker take on the superhero genre to contrast with Action.
4. Swamp Thing - I hesitate slightly because there's a lot of exposition in this book at the start, and even though I got into it without much knowledge of Swamp Thing history, I did at least feel grounded in the DCU. So I would warn the reader that the first few issues are heavy on the explanations, but I think the richness of the world and the story once you get into it - in addition to the use of panels and the fantastic art, means I'd recommend it.
5. Animal Man - I'd recommend this out of sheer quality and also as an example of genre diversity, breadth of artistic style and an example of the way shared universe comics can interact while still being independent (with Swamp Thing).
6. Batwoman - For the art alone, this should be on the list, but it's also a good story and the supernatural and military edges to the character both differentiate her from Batman and present a slightly different take on a powerless masked vigilante.
7. Stormwatch - It starts a little unevenly, but it grows into something truly strange and odd and fascinating. It's wacky and insane and chaotic, and a little less heroically idealistic than most cape stories and I think it captures the brilliant edge of "what the hell is going to happen next?!" that good comics can in a way fairly few other books right now are managing.
8. Demon Knights - Strong characterisation, morally ambiguous protagonists, beautiful art, genre diversity in terms of historical fantasy, a plot that is wheeling out into something fascinating both within the series (with Shining Knight's Quest tying in to that of the Queen) and outside with another example of a lowkey crossover with Stormwatch that plays to the strengths of a shared universe rather than the weakness of demanding the reader keep up with a hundred series.
9. Justice League - Not a favourite of mine, but it's big, bold, easy to understand, pretty to look at and is the anchor book of the DCU dealing with a lot of the high profile characters. So for a new reader it should probably be on the list.
10. The Flash - I'm actually not reading this book anymore, but the art is undeniably gorgeous and since I'm now down to a handful of higher quality books that could all vie for this spot, might as well put a book that really showcases the visual nature of the medium, since we're talking about a newbie. Plus it's a classic cape story.
Other books I would have liked to include, or might substitute into that tenth spot based on the personal taste of the reader would be Blackhawks for fun military action and transhumanist shenanigans, Static Shock for a younger teen hero, Batgirl if the person wanted more Batverse, All-Star Western if they like Western stuff, Justice League Dark would be on there already in the #10 spot if I didn't think it was a little new-reader unfriendly without even Swamp Thing's mountains of exposition, but if the person liked the more Vertigo twists to things, I'd suggest subbing this in, and finally Birds of Prey if they want it more skewed towards team books.