Don’t rent a car. You won’t need one unless you have mobility issues.
Get a 3-day transit pass at the airport, or at any metro stop. Reload it with 1-day passes once that expires. That’ll give you unlimited rides on all the buses and trains within the city. There’s a bus (747 line) that’ll take you from the airport to downtown.
The trains within the city are great. Looking at a map, the metro system doesn’t seem very extensive compared to other cities, but it got me close to everywhere I wanted to go. The trains came every 5–6 minutes in literally every stop I visited on every line. I rarely had to wait more than 3 minutes for a train.