The 1st opening riffs to BEASTIE BOYS "no sleep til Brooklyn" & KISS's "War Machine" were probably the 1st 2 songs I ever tried to play!
Other riffs I tried to learn on my own when I 1st started playing:
KISS - "Burn Bitch Burn" (non make-up era from the Animalized album),
IRON MAIDEN - "2 Minutes Til Midnight"
MEGADETH - "Wake Up Dead"
AC/DC - "Shook Me All Night Long"
METALLICA - "Am I Evil"
JUDAS PRIEST - "Heading To The Highway"
TED NUGENT - "Cat Scratch Fever" (but who hasn't)
The reason I say riffs is because I never really tried to learn whole songs! It was always the opening riffs that made the most impact for me!