Tyres made of pure rubber or foam are ok. Tyres with silicone oil are not allowed. The silicone oil from the tyres will make the track very slippery. Silicone tyres are good on carpet that covered with silicone oil and rubber mixtures.
If you are after speed and easier control, foam tyres are the choice, not to say foam must be better than rubber. Rubber (without silicone oil) tyres are good on RCP track. Kyosho cup official tracks only allow pure rubber tyres in their races. Recommend you to go up and have a trial first.