Lionel has traction tires and lists them by size of the tire not size of the driver. You want a tire smaller in diameter than the wheel. As for the battery you don't really need one. It just there to maintain sound if the engine loses power at a dead spot. It has no way to charge a battery so skip rechargeables and BCRs. An alkaline is fine. Just remember to swap them out about every 5 years.
Pete