It will be hot in July, really hot. Go out early in the morning, eat lunch and do like take time off in the heat of the afternoon. Look for a local guide, you can hire. private guides, they can get you into places you can not go, and get you past the lines. Try to stay with small tour as the extra fee to be in a small group is worth the investment.
Walking shoes are a must, with good grippy soles. The marble is old and now polished to a slick surface, so they can be very dangerous. Many of the staircases do not have hand rails. Surfaces are uneven also.
Just keep your head on your shoulders be aware of your surroundings and people around you. Have your wife invest in a PacSafe purse, don't carry anything you would not want to loose. We switched my wife's rings and earrings over to the low cost costume stuff. She did not care if they where lost, and I did not care either.
Umberallas make a nice shade for where there is not shade. Water is safe to drink, but bottle mineral water is cheap and taste better. It will be listed as still, sparkling has bubbles and if you don't like carbonated water you might be in for a rude drink.
Big backpacks are not allowed in lots of the venues, and will be searched. Pack light for your tours.
If going to regions sights, shoulders and knees have to be covered so no boy shorts Kent
Watch where you take photos, lots of military and they don't take Kindly to photos being taken of them.
They have the right to destroy your camera footage. In some cases that means they will destroy your phone, or digital camera.
Hop on and Offs are a great way to get around.
My order of visitation would be Vatican and all its glorious chapels, you will need to be covered for this shoulders, and pants bellow the knees. Check with the guide to see what is being allowed. Then the coliseum, then do the ruins, then everything else.
In the corporate world we send people over with burner phones and laptops. I have been using older iPhones and ChromeBooks. When they get back, I literally toss them into a wood chipper. It is fun for me and I don't worry about the carp they might have picked up while outside the US.
Enjoy the trip it is a great place to see.