Don't wipe the screen, even with a microfiber cloth. If there are any carbide particles on it, they'll scratch the screen like a hot knife will scratch butter. Just blow off any dust for the next week or two.
When you apply the screen protector, first use tape (masking tape, cellophane tape) sticky-side out to pick up any dust particles on the screen. Then use a lens cleaner sprayed onto a microfiber cloth to clean off the fingerprint smudges. Then apply the screen protector. (A speck of dust too small to see can cause a 1/8" bubble in the screen protector.)
If you really bring a cellphone to a beach, or any other dusty or sandy (or especially a wet) place, put it into a zip lock bag (the kind you press closed, not the kind with the "zipper") and zip it shut. Then place that bag, ziplock end first, into another ziplock bag and zip it shut. The phone will be more dustproof and waterproof than a water resistant phone. (If you leave enough air in the outer bag, it'll float. If you drop it overboard, and you have a net handy, it's just an "oops", not a disaster.) You can still use the phone through the two bags.