Driving in Puglia

I’ve used both; it should come down to your personal preference. Perhaps your phone plan as well, though you can download offline maps in advance. What do you prefer in your everyday life, and is your travel partner a willing and eager navigator using the phone?
Do you have experience navigating ZTL? Feel free to post your itinerary for tips.
Puglia was our first driving trip and now it’s our usual plan, as we go to rural areas and villages/parks more than cities. In Puglia, it’s just a lot of traffic circles on rural roads other than the main highway along the coast. Have a plan for parking, and you’re all set!

I don't use the car GPS even if it might be available in certain models I've rented. The built in GPS systems don't warn you about speed cameras, therefore they are useless to me.

If you rent a compact or economy, you probably get only CarPlay, to which you would connect your phone and then use your phone navigator. Make sure you have a cable to connect your phone to CarPlay. You need a cable USB A to USB C for CarPlay connection.

Although my preferred navigation app on my iphone is GoogleMaps, however in Italy I often use Waze, which I have set up in the Italian language (so the pronunciation of the streets makes sense to me, and is not some Italian gibberish pronounced by a foreigner).

Waze is part of Google now, but it is more accurate and warning you of all fixed speed cameras (called Autovelox or VeloCar). Hidden speed cameras in Puglia are not as ubiquitous as in Tuscany, but there are some. Also they often set up mobile cameras aboard police patrol cars, so they are not fixed, but are set up at different spots. Waze warns you of those as well because the information is fed to the app by other motorists and 100% of Italians use Waze, therefore the information you get is the most up to date. I use my preferred GoogleMaps only on the toll freeways, since the toll freeways don't have speed cameras, or are extremely rare, but rather only the Speed Tutor System cameras, a system which takes photos of all cars every 5 km and calculates the average speed in that 5km segment to determine if you deserve a speed ticket for that segment. GoogleMaps is just as good at warning you of the Speed Tutor System.

Or stick to the speed limit.

As Laurence Olivier said to Dustin Hoffman when the latter banged on about The Method “ Try acting, love, it’s so much easier”.

Thanks to all of you.

Make sure all drivers have an IDP- required by law
We were asked to show at rental agency last 2 rentals in Italy
Get at your local AAA before leaving US
About $20

I've been to Puglia several times; the first two times we used paper maps!

Now we always get the GPS that is installed in the car.....

We just returned from what was, I think, our sixth trip to the region. As said, above, driving is so easy. I do not drive much at home and even I found it a pleasure to drive on those roads...parking is much more difficult than driving.

Or stick to the speed limit

The problem is to know what the speed limit is.

Sometimes the posted speed limit is not signaled too clearly, as the posted sign was long before the speed camera, and you forget what it was, so in that case the navigator will also tell you what the speed limit is in that segment of the road. It's not 100% accurate, but for the most part it is.

In any case, if you go 5km (3 miles) above the speed limit, the camera will take a photo and you will receive a fine. 3 miles per hour above the speed limit is very easy to miss, especially because the posted speed limits in Italy are often unreasonably lower than necessary for the type of road (probably because it's easier to get people trapped that way).

For example in this image you can see that this 4 lane divided freeway in Florence has a speed limit of only 60 km/h (37 mph). It's not that easy not to get distracted and go over by 3 miles per hour. That means that on this freeway, if you go over 40 mph you get a ticket and there are 4 cameras nearby, 2 in each direction.