Lots of good recommendations, just going to say that I probably wouldn't choose spring to start hiking in the white mountains. Wait till summer... Shoulder seasons can be rough, particularly for a beginner... You've got mud, disintegrating monorail, difficult water crossings from the snow melt, and you're still going to be hitting icy/snowy patches where you need foot traction. You can also get temperatures ranging from below freezing to eighty degrees, with big swings in temperature in a single day.

If you want to start in the spring, try southern NH (still likely to hit mud but not as treacherous otherwise).