I would still book a hotel in downtown DC. Early on a Sunday AM, it's a 10-minute Uber out to DCA vs. a 5-minute ride from a DCA hotel, due to the traffic pattern. The tradeoff is the difference between a sterile airport/office park vs. downtown DC with great restaurants and a good time.

I would Uber to a DC hotel near whatever site you pick, drop your bags and head out to whatever it is you want to see and dinner. Depending on what that is, you might be walking. In the AM, hop at Uber back to DCA and you've had a great time and no hassle.

Car rental at DCA is as convenient as it could be under the circumstances, but that does not make it convenient. There are no HOV lanes at any time between DCA and DC, especially on weekends, but traffic on Saturday PM can back up. Parking at nice downtown hotels is rarely included and can run $40-60/night easily. So, why settle for some place based on cheap parking?