I would suggest a carpet with a slight pattern on - just mottled rather than horrible big flowers or similar

Just two shades of the same colour maybe with a stippled effect. This doesn't then show up dog prints, muddy boots which have come in by mistake etc. We recently had a visit from a party coming round to see our smallholding. They didn't take their boots off before walking all over my Persian rug

Of course that doesn't show the dirt at all but I was still miffed - and it's certainly not that I'm overly interested in housework

but the rug is not wash-fast.
Our main floors are wood (oak) which is not slippery. I have asthma so we have taken all the carpets out as they were always dusty.
Choose a carpet which is shampooable. I've no idea of the colour. We've lived in lots of different houses with a wide variety of carpets from hideous '60's overwhelming patterns to a dark brown which showed every single mark. My favourite was a mottled gold, in pure wool (no stinting for the RAF!) but we only lived there for a few months before we were posted elsewhere.
It's difficult isn't it! You want something that looks smart but which you won't hate in a year or two. Fashionable colours to suit your walls will seem awful in a few years, but a safe beige is cowardly and boring (apologies to those of you with beige carpeting

)
I love those loopy wool carpets - forgotten what they're called - which can be beige-y but are mottled so look lovely. I'm not sure how well they would wear or shampoo though.
Let us know what you choose in the end.