To run tyres without additive you will need them to be very soft, and that means they will not last long. They'll wear quickly and chunk easily if you clip a track marker. Finding the right tyres for that is probably not possible these days, everyone makes tyres for additive.
The best tyres for life are either Xceed or Contact. Having tried both, the Contacts just shade it as they are glued better. If your carpet is low grip, then you should try Xceed soft rear and medium front, or Contact soft-pink rear and magenta front. If it is high grip, then medium/medium Xceed, or pink/pink Contact. For low grip it's pink rear/double pink front in Jaco, Parma or Mobgums (all the same wheel and tyre) and pink rear/magenta front for high grip on those makes. Jaco are about £12 a pair, Xceed and and Contact £8 a pair.
Additive should be CS High Grip. Don't use too much, a small amount applied with a paint brush will do just as well as slapping it on and making the tyre soaking wet. Try to get 20 minutes on the rears (full width) and 10 minutes on the fronts (half width, from the inside) before wiping them dry with a towel.
Take Rudolf's offer and you'll soon find something to suit your needs. HTH
