also, you can check out your basic chords. First, you have your I, ii, iii, IV, V, vi, and vii chords. Captial letters always indicate a major chord and lowercase is always minor. Each of those chords are very easily derived and all use notes in the key you are in. To play the I chord you just play 1, 3, and 5. To play the ii chord you play 2, 4, an 6. iii is 3, 5, and 7. So on and so forth for the other chords. The natural minor chords is the ii, iii, and vi chords and your natural dimminished chord is the vii chord. Natural majors are I, IV, and V chords.
Now, there are more to chords than just I through vii. You can also play special chords. Some your might want to toy around with are:
augmented chord: two stacked major thirds. (1, 3, sharp 5(C, E, G#))
dimminished chord: two stacked minor thirds (1, flat 3, flat 5(C, Eb, Gb))
M7 chord: Major chord with a major third stacked on top (1, 3, 5, 7(C, E, G, B))
Dominant 7 chord: Major chord with a minor third stacked on top (1, 3, 5, flat 7(C, E, G, Bb))
There are an infinant ammount of possibilities for chords. The true definition of a chord is 3 or more different notes played at the same time.
As for very basic chord progressions, the I, IV, V came up. You could also try playing just four consecutive major chords such as C, F, Ab, G.
Hope this helped.