All sport is free and you should get plenty of opportunities to participate. Adventure training is subsidised so that you will pay some money towards travel/keep. You get extra leave each year to participate in adventure training.
If you are good at a particular sport then you may take it to the highest levels. Last olympics the RN had a few people taking part include a gold medal winner. The up and coming winter olympics will the the bobsleigh team mainly made up of Royal Marines.
If you enjoy sport you will get plenty of opportunities through a career within the RN