Based on your stated parameters, (large group, international travel newbies, August, under 4k/week) your three best options are:
1. Aruba - a very US-like experience, large resorts and plenty of condo/AirBnB options, all-inclusive isn't necessary, island is safe to roam and explore, Fits a lot of budgets. Cons, better resorts can be expensive especially if food/drinks are included
2. Dominican Republic - value for $, many large all-inclusive resorts, caters to Americans. Cons: mostly bound to resort property, August is hurricane season.
3. Any Caribbean Cruise - All inclusive, easily under 4k per couple unless you drink a ton without a drink package, everyone can do there own thing and still spend pleny of time together. Recommend the larger, newer ships. Southern routes are best, followed by eastern and western. Carnival, Royal Caribbean, Norwegian, Celebrity are all fine for groups, enough variety to pick the best ports, itinerary and price. You can link all the reservations together for dinners etc, 8 cabins usually gets you a discount. Cons: cruising is not for everyone, getting 10 chairs by the pool isn't going to happen. Someone in the group will need to coordinate the reservations so that the group can relax once onboard.
Any all-inclusive will be able to accommodate your group to some degree, but the first time travelers may be uncomfortable with the large disparity in the standard of living between the tourists and locals in some of the more off the beaten path locations. If the plan is to stay on resort, then they are pretty much all the same but half the point is exploring. If you stick to Viator rated tour operators, anywhere you go will be safe.