Besada makes some great recommendations. That is classic Legion, which has popped back up from time to time, after the Reboot versions that happened. The one I usually suggest to new readers, both because it's a fresh jumping on point and is well collected, is the Mark Waid Threeboot Legion. It's a slightly different take on the concept but keeps the core values in place.
The reading order is:
Legion of Super-Heroes, Vol. 1: Teenage Revolution
by Mark Waid
Legion of Super-Heroes, Vol. 2: Death of a Dream
by Mark Waid
Supergirl and the Legion of Super-Heroes, Vol. 3: Strange Visitors from Another Century
by Mark Waid
Supergirl and the Legion of Super-Heroes, Vol. 4: Adult Education
by Mark Waid
Supergirl and the Legion of Super-Heroes, Vol. 5: Dominator War
by Mark Waid
Supergirl and the Legion of Super-Heroes, Vol. 6: The Quest for Cosmic Boy
by Tony Bedard
Legion of Super-Heroes, Vol. 7: Enemy Rising
by Jim Shooter
Legion of Super-Heroes, Vol. 8: Enemy Manifest
by Jim Shooter
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A good one off trade that's great for both old readers and new is:
Superman and the Legion of Super-Heroes
by Geoff Johns