Chords suited for electric guitar
There are many differences between an acoustic and an solid-body electric guitar and some of these things affect the way you play chords in these cases.
Electric guitar with clean tone
Then you have the amp at the “Clean” channel, there are no big differences from using an acoustic in terms of chord playing. The open chords and barre chords will sound good in both instances.
Besides from strumming, you could play arpeggios with different effects including chorus and delay on your electric guitar. If you are uncommon with arpeggios, here is a basic example in tablature:
The chord shapes are alternatives from the standard.
Electric guitar with distortion
Playing with distortion makes the strings less articulated. That could result in a blurry sound from open and barre chords. It most cases it won't sound good playing on all six strings with gain and distortion.
That's why power chords are often preferred when playing on the electric guitar. These chords involve only two or three strings and makes the sound enough articulated even with heavy distortion.
Learning the palm muting technique is fundamental when using power chord. This is a standard feature in rock, punk and metal.
Nothing stop you from playing regular open chords, but in many cases you should strive for only hitting the lowest strings. Some open chords will sound better than others in combination with distortion. For example A, D and E are well suited to form cool rock sounding riffs:
Try to only play on the lighted strings for better sound on your electric guitar. But obviously you should not be inhibited by this to the degree that you can't strum freely. If you, for instance, play on the highest string on the D chord that's no catastrophe.
See all articles about guitar.