I'd have a tough time deciding between the NYT and WSJ next, especially since the editorial/opinion section of the WaPo is the least valuable to me (informed opinion is something you can get everywhere on the Internet for free).
(WaPo vs. NYT was basically a coinflip decision for me, but doing WaPo and then NYT would probably create a pretty significant overlap, and WSJ wouldn't. On the other hand, the NYT is a substantially better site than WSJ).
WSJ + WaPo is great IMO. My morning routine is WSJ, FT, WaPo, and sometimes NYT. The NYT is my least favored source partly because they skew too heavily toward my biases and I prefer reading high quality news from alternative perspectives more. YMMV.
(WaPo vs. NYT was basically a coinflip decision for me, but doing WaPo and then NYT would probably create a pretty significant overlap, and WSJ wouldn't. On the other hand, the NYT is a substantially better site than WSJ).