As a "jersey shore" girl I would suggest a gulf beach over one on the Atlantic unless you and your children are Ocean Swimmers. The Atlantic Ocean beaches can be rougher than those of the gulf. The water gets deep faster and the waves and undertow can be very overwhelming to someone not accustomed to them.
St Pete Beach is great. We leave Orlando 9:30ish, arrive 11:00. Swim and beach for a bit then we love to go to Bongos for lunch, let the kids swim a bit more after lunch. Then head over to Johns Pass to walk around the shops, have some dinner and then head back to Orlando. If you go on a weekend day a lot more going on. Bands, festival type events, etc.
We are going down the first week in March and the water temp is on the cool side. Probably high 60's. A few degrees warmer than the AO beaches but not by much. My kids don't seem to mind though.
Whatever you decide, enjoy!