I point up, down is uncomfortable for me. It does up into the waistband. When my dad gave me my first jock at 13 he said to point up- so I always did. And if I get hard - it doesn't hurt as much.
I have 2 unlined board shorts for the beach. I use a Bike swimmers jock under. I also have a blue Cellblock 13 but it doesn't have as much support as the Bike. https://www.bikeathletic.com/collections/jockstraps/products/swimmer-jockstrap-white