Hello Kathy
The Paphos Region is far more rugged and natural than the East Coast.
Most of the beaches in this area are shingle or a mix of sand & shingle.
Some sandy beaches can be found but tend to be very small, in little coves.
The beach at the rear of the St George's Hotel is man made but consists of crushed shells, however it is fantastically clean and the break water makes swimming very safe and clear.
The best beaches in the area are probably found @ Coral Bay - 20 mins on the bus from Paphos Harbour. We tend to go here with the little ones to build sand castles.
It tends to get very busy on a Sunday with locals but in October it should not be a problem. We went for a week last year in October, the water was great for paddling - the little ones loved it.
Paphos is a great place to visit later on in the year as it is still busy but not crowded.
The weather is warm but not too hot - but it all depends on what you like and what you intend to get out of your holiday.
Anyway - good luck with your search.