I don't climb 5.14, but Proper Soul would be on my radar if I did. I know the New well, and for it to produce a 5.14, the quality of stone has got to be perfect. The Cirque is a gorgeous area and the New is an amazing place. Come in the fall!
Another NRG vote: Mango Tango. Looks like a sweet arete!
I've always thought that Mango Tango is the most beautiful line at the NRG. I'm not sure I'd call it a best "first" 5.14, though. While Proper Soul is quickly becoming the 2010s version of Apollo Reed, Mango Tango just sits down on the Meadow, gathering cobwebs and smacking down good climbers. A while back, I recall one rejected suitor angrily writing "5.14c!" in chalk below it.
(this is all just hearsay; I, like most folks here, am not a 5.14 climber)
That Joel Brady video is RAD. Makes me want to jump in the shitbox and head to the rainiest, muggiest, most miserably often weather-cockblocked Promised Land a guy could ask for. Looks like Mutiny on crack. Awesome.
Haven't tried any .14s so no helpful beta on climbs, but if you want to find good .14s, I'd contact people that crush .14 like there's no tomorrow and have taste. Joe Kinder has a blog and has climbed a few dozen at least, bet that's a good place to start-Joe's a cool kid and would for sure email you back a good route or 3 to start out with.