Electric guitars are pretty simple things at their heart.
Aficionados worry about things like the tone characteristics of the body, but that's a really subtle effect, and budget guitars are unlikely to benefit from good enough materials for that to matter.
The absolute most important factor is action and intonation. Make sure that the neck is straight, the action is acceptable all the way down the fretboard, and that the intonation is good.
One basic check is to play a harmonic on the 12th fret, then an octave. They should have the same pitch.
It's good to have two pickups, so you can choose different tones. The pickups have a much bigger impact on the sound than the body. However, it's fine to start with cheap pickups, since they can be replaced with fancier ones at a later date very easily.
Cheap electric guitars can be very well made nowadays. Check for obvious cut corners, though. Reject anything with badly finished frets. See that the bridge looks nice and solid. Make sure nothing wobbles where it shouldn't.
Decide whether you want a tremolo arm. Many guitarists go their whole career without using one. Hank Marvin never stopped wobbling his. They have a reputation for making it harder to keep the instrument in tune, and that's more likely the cheaper you go -- but if you want the effect they provide, by all means go for it.
Don't buy a super-cheap practice amp. They sound awful. It's better to put an amp-modelling pedal through a hi-fi -- slightly more expensive practice amps such as the Roland Cube are fine too.