Welcome to the board.
Make sure you peak your head into
www.adkforum.com as well. The 'dax have a lot to offer in addition to the high peaks.
As for your first peak. If you are really going for it, I would totally emerse myself in the High Peaks for a weekend, and see how you like it. That is, if you have the equipment for backpacking. Johns Brook Lodge area makes for a good campsite, with options for paid lodging, tenting, and staying at a leanto. There are many peaks over 4000 nearby, all have great views. Big Slide is a good starter peak, and if (and only if) you have some mountain experience, you may give Gothics a try. Marcy is not out of the question from JBL, and many people choose her as their first.
If you don't want an overnighter, most people choose Cascade and Porter for their firsts. Wright and Algonquin also make good first summits, as does Phelps, although Phelps has a long lead-up.
Whatever you do, make it YOUR hike! There are infinite possibilities for your adventure. Enjoy!
-percious