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.

I'd avoid a light overall colour - we inherited a fairly new pure wool in a light beige and it's a nightmare to keep looking good. I'd give anything for my old house's slightly mottled berber, but I'm not sure that would suit the style of your house/room. I'd go for something that you like and which would go well with the type and colours of your bed linen. Don't go too dark either - I also lived with dark grey in a bedroom and it showed every minute light fluff from clothing (not to mention the white underbelly fur of the cat we acquired.)

What is the cheapest carpet type?

We have bremworth 100% wool sisal in bedrooms and on stairs. The pic of the stairs attached is carpet that has been down for 15 years. People & a crazy dog up and down them and more than one morning coffee spilled on it. It is only just starting to show a little wear now - slightly lighter parts on some of the treads.