Sounds like you will be wanting to stick to the central and eastern valley, so I’ll keep my focus there. DVNP is a far flung region with huge variations in elevation, weather, topography, flora and fauna. It’s a large place that requires multiple visits to see it all.
I’d recommend keeping an eye on the DVNP website for road info and suggestions to visit.
Death Valley National Park (U.S. National Park Service)
Dante’s View. Due to elevation, will be chilly and might be windy.
Artists Drive.
Sand dunes near Stovepipe Wells.
Visitor Center at Furnace Creek.
Badwater.
If you have the time, a drive up into the pine forests just west of the valley to see the historic charcoal kilns is a treat. Probably snow up there by now. Paved most of the way with several miles of maintained dirt the remainder.
Not far from Pahrump is the China Ranch date farm.
China Ranch Dates, Inc.
For the unusual, stop by Death Valley Junction, which was a major railroad stop in history. Though Marta Becket died several years ago, she danced nightly even to a theater of empty seats for decades.
Marta Becket's Amargosa Opera House and Hotel
Marta Becket's Amargosa Opera House and Hotel
First link is about Marta Becket, the other about the opera house and tour info.
Biggest issues with rental cars are tires. I’d keep them on the pavement. Look at the fine print of the rental contract. Some say that off road use will void something. Off road often means maintained dirt roads. AWD rental cars such as the Rogue often are really 2WD. I’ve heard of rental companies disabling drive to the second axle.
The north highway accessing The Racetrack is still closed for the foreseeable future. I wouldn’t take a rental in there, but they often are found. The road is notoriously washboarded and often has large gravel.
The road in from Beatty has recently been reopened, though parts of it are still graded gravel.
Have fun!