Hi A., congrats on your upcoming vacation, sounds like fun. I can't recommend a specific resort in Panama City, but we are in the hotel business, so I'll give you a few pointers when looking.
First of all, tourism is still a little slow here in the southeast, so don't be afraid to haggle with the resort on the price. Second, be careful about using second party rental agencies. I can't tell you how many people's vacations I've seen ruined because they couldn't get the services they needed (ie: towels, linens, maintenance, etc.) It's almost always a better idea to book the room directly with the resort unless the secondary rental company has an on site office (and they rarely do.)
And "beware the timeshare." You may receive a phone call inviting you to come to a free lunch or offering you "$100.00 for and hour of your time." Don't do it. Time share sales people are trained in high pressure sales, and they want to get at you while you have your guard down (ie: relaxed and more agreeable).
Travelocity.com is not always an accurate guide when selecting a resort. I booked a place in Ontario because it got rave reviews, while the nearby casino hotel got bad ones. Once we arrived, I wished that we had stayed at the casino hotel as it was far superior.
Also, sites like Expedia.com charge hotels 30% of the room rate for bookings. Most hotels will give you a better rate if you call them directly.
As a general rule, the more despriptive the website is, the better the hotel is. Avoid places that don't post a lot of pictures. The better the product, the more the seller is going to want to show it off. At the very least, they should include recent photos of the amenities and the guestrooms.
Hope some of this has been helpful. Good luck to you all, and I hope you have a great time!