I currently use a few different cards depending on what I'm buying to get the most out of it. The barclaycard is great for general purchasing. I like the amex gold card for dining and groceries as you get 4x points per dollar. The Chase Sapphire for travel, and the chase freedom for the rotating 5x points categories. You can get a ton of value by transfering chase or amex points, but it's a lot more work than the ease of using the barclaycard. I also recommend always signing up for the rewards program of any airline/hotel you use. I hope this is helpful!
I think the Barclays Rewards we all use is good way to supplement what travel we cannot book on points with other hotels and airlines. I think building up "buckets" with different airlines and hotels are best strategies to utilize so you can be flexible as possible for future travel. Once you have enough points in one "bucket", work on another program.
For domestic travel, I find it depends on where you fly out of that works best for everyone. Focus on that airline to generate enough points. I find Southwest the most flexible as it allow trips to be booked ahead of time and cancel for free. Getting Southwest points is easy if you can get their Chase credit cards.
For hotels, I like Hyatt. Cheaper point redemption and you can transfer Chase Ultimate reward points and get Hyatt credit card to maximize point total.
Hope this helps!