Most beginner guitarists start by learning the same fifteen chords, usually called the “standard fifteen.” I’ve also heard them called the open chords because they make use of open strings and are thus easy to play:
A A7 Am
D D7 Dm
E E7 Em
It’s not much good to just memorize the standard fifteen chords without musical context. It’s better to learn them grouped together into keys, so you can hear how they relate to each other. Family Guy explains how this works using the key of G. I apologize for the filthiness of the opening joke, but then it actually turns into a good music theory lesson.
Here are the standard fifteen grouped into various useful major, blues and minor keys. Pick a row and try the chords within it. They’ll sound good together in any order and in any combination. The first chord in each row is the tonic chord, which feels like home base.
I ii iii IV V vi V/V V/ii V/vi
C major: C Dm Em F G7 Am D7 A7 E7
G major: G Am -- C D7 Em A7 E7 B7
D major: D Em -- G A7 -- E7 B7 --
A major: A -- -- D E7 -- B7 -- --
E major: E -- -- A B7 -- -- -- --
I7 bIII IV7 V7 bVII C blues: C7 -- -- G7 --
G blues: G7 -- C7 D7 F
D blues: D7 F G7 A7 C
A blues: A7 C D7 E7 G
E blues: E7 G A7 B7 D
I V/V bIII iv IV v V bVI bVI7 bVII
D minor: Dm E7 F -- G7 Am A7 -- -- C
A minor: Am B7 C Dm D7 Em E7 F -- G
E minor: Em -- G Am A7 -- B7 C C7 D
For more adventurous sounds, try mixing chords from different keys together. Trust your ears and have fun!
Update: once you’ve mastered these chords, maybe you’d like to tackle the pentatonic scale.
Further update: it was pointed out to me by commenter Bruno that the roots of the blues chords spell out the minor pentatonic scale. I hadn’t even noticed that. Pretty cool.