Ensure you have good footwear for the walk to the beach and a carrier for your kids (if they are at that age) as it is not pram (stroller) accessible. Also, you might want to pack yourself a picnic lunch to enjoy on the castle grounds.
You need to pay for parking practically everywhere in the U.K. Barafundle Bay Beach is in the National Park and costs £5. The castle parking is at a pay meter and costs roughly £1/hour. Make sure you have cash or coins to pay for parking.
Wales can be quite wet and rainy. Be sure to choose a sunny day to get the best out of Barafundle Bay Beach and Pembroke Castle. Also, try to time the day to enjoy a picnic lunch on the castle grounds. There are lovely grassy areas to sit and relax. Whether you do the beach before or after visiting Pembroke Castle, this is up to you.
Summer would be the best time of year to enjoy this mini-adventure.