Tyres or chassis?
Tyres, I'd use Schumacher Minipin Yellow compound. These will provide high traction on the carpet, and a little loose on the slippy. The contrast between the two surfaces will be high
A lot of people also us the Schumacher Minispike Yellow Compound. These will offer higher grip on the slippy floor, and reasonable grip on the carpet, with the contrast between the two surfaces will be lower.
Regarding chassis, go with whatever is popular and well supported at your local club. I'd like to think one of the leading UK chassis manufacturer's, from a UK model shop.
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