I've had 2 TKRs over the past 5 months. I did my worst, most misaligned, less stable knee first. For me, that was my right knee. I did the right knee in July, since I knew I'd end up relying on my left knee (it also had considerable pain and misalignment, but was stronger) for the first several weeks after surgery.
I have a few steps to get into my house and need to climb a full flight of stairs to reach the bathroom and bedroom. My left knee held up fine to support me through the 1st recovery. Had the left TKR in early November. Both surgeries went well and I can't get over just how wonderful it feels to move, stand and live without the chronic arthritis pain.
Based on my experience, I'd start with the least stable knee. Good luck - you can get through this!