The best way to get from Havana to the hotel in varadero is with a taxi. For a private yellow air conditioned taxi, the cost is 95cuc (95usd). The distance is 180km and takes about 2 hours. I can organize this easily.
The caves are about 25km from the hotel in varadero. It’s not a long trip. It should take about 30 to 45 minutes. We cannot organize a specific taxi for you, for this trip. There will be taxis at the door of the hotel and you can ask a driver to take you to the caves. It would cost about 30$ to 40$ for the trip. Maybe you negotiate with one of the drivers and offer 50$ for him to bring you to the cave and then wait while you explore and then drive you back. It would be a fair price. You would negotiate directly with a driver at the hotel.