Hello!
I'd pay 300$ or less for the speakers, and not more than 100$ or 200$ for the earphones or headphones.
I would like them to be able to sound deep, even sub bass range. Don't know if I'm asking for sub bass and linearity of sound (like a studio monitor) AND asking for good bass is a contradiction. Generally hi-fi fans are all for bass boost and coloring of the sound. I have a hunch linear sound would be better for metal all around, since I read hi-fis can't go deep enough and overcompensate with a thumping, low quality bass. I have an old 2.1 speaker set I can't even find on the web, wouldn't post images of it ATM.
I would be listening to metal sitting at the desk, or while doing chores around the house, exercising, etc. I would probably switch to headphones/earphones during if the speakers are near-field and I'm in another room, exercising, and the like. My room where my desk is measures like 10 square meters.
Until now, I have been looking at the Edifier R1280T. I live within the EU.

You may want to have a look through this old topic first:
viewtopic.php?f=2&t=123334&hilit=Earphones