If your intended application is desktop production speakers, you will want near-field monitors.
These are examples of near-field monitors. They are designed to be as neutral as possible and have a decent sound field in close proximity to the speakers. If you are serious like you say, I would advise getting a pair with good bass extension so you don't have to rely on a subwoofer as much for monitoring the bass. For monitoring, I would want to take the subwoofer out of the equation as much as possible, just relegate it to deep bass. Go for some monitors with 8" woofers and extension down to 50 hz if you can. Cross em over at 60 hz to the subwoofer.
If you intend to make bass heavy music, as I would infer from the phrase experimental electronica, my advise would be get a subwoofer with good bass extension. This will widen the palette of sound you have to work with, and it will also let you know if there is inappropriately deep bass in the mix- this can happen and it is something to watch out for. If I were you, I would also get a decent pair of headphones, to check your mix. Headphones can reveal stuff that speakers have a hard time with, but speakers can convey a soundstage that headphones can not, so its important to have them both when dealing with music production.
Monitors are typically powered, so you won't need an amplifier, and you wouldn't want something like a surround sound AVR anyway. You wall want a good sound card though, what kind of sound card are you using?