This is the room in question the furniture will be replaced with a creamy white suite but the carpet will also go when the new furniture arrives

I think charcoal grey is the most popular carpet colour at the moment. I've recently been trying to make the same decision between a more "beige" carpet and a "grey" carpet. I ultimately decided to go with beige. I think it will still show up lint and fluff, but less so than charcoal which I've seen in other houses and which seems to show almost everything. If I had a larger budget, then I would have gone with a woolen carpet in beige with specks/flecks of colour throughout. I was unable to find any non-woolen carpets which had specks/flecks of colour. As you're not looking to spend a lot, I'm guessing that a woolen carpet will be outside of your budget also. I think whoever regularly does the vacuuming and cleaning in your household should get to decide as they'll ultimately be responsible for cleaning the carpet whatever colour is chosen.

More Carpet pics. Only my only 2 favorite options are shown in the photos. As you can see different spaces = different shades visible. I should add that our staircase and upper floor will be carpeted. Ground floor is mostly tile - only a kids/multi-purpose room and bedroom will be carpeted. These rooms sit next to tiled spaces.

I like the grey against the reddish floorboards. With pets and teenagers, I wonder if darker would be better? I installed pale carpet pre-parenthood... worse mistake... will be going a darker shade next time!