We strongly recommend against renting cars as parking in downtown Oakland is expensive and difficult. Ride sharing apps are a great option in Oakland. You can use these links to download Lyft or Uber and receive free credit for your first ride.
If you think you'll need to drive, car-sharing services like Getaround and Gig will probably end up being a cheaper option than a rental and paying for parking. Using Getaround folks rent out their personal cars by the hour sort of like AirBnb for vehicles. Gig has a fleet of cars scattered all around Oakland and the East Bay. You can pick a Gig car up in one spot and leave it in another all within a wide designated zone. Here a links for credit on your first Getaround or Gig rental.
Oakland also has a bikeshare program with stations around downtown called FordGoBike. For a flat daily fee you can rent bikes for as many 30min rides as you want.
There are also electric scooters for rent all around Oakland. Using an app you can locate and activate a scooter. It usually costs $1 to start riding plus an additional fee based on time and distance. These scooters are hella fun but be careful you can crank them up to almost 20mph. Here's a referral link for some free ride credit for Bird and Lime.
BART is a great option to get from the airport or to San Francisco but not necessarily the best for getting around within Oakland. Within Oakland the bus is a better public transit option, check out AC Transit schedules. There is also the Free B, a free shuttle that runs up and down Broadway right past the hotel.